Or it might not, say the Coen brothers.

Securing an audience with the Coen brothers is like being invited to dine with lions. It might be a blast, or it could end in blood, sweat and sawdust. Their reluctance to talk about their work and private lives has become part of the Joel and Ethan legend, along with the four Oscars, the Cannes triumphs and the cast of modern Hollywood greats who queue up to be in their films.

Yet here they are, musing over landscape and character, discussing The Wizard Of Oz, and trading thoughts on the Tommy Lee Jones-ness of Tommy Lee Jones, star of No Country For Old Men (“Not a pleasant fellow,” says Joel). It’s a weird meeting, not so much chowing down with lions as herding cats, but it’s happening. At several points there’s even laughter, as if this interview lark is not such fresh hell after all.

Something odd is going on with two of ­cinema’s strangest dudes. To coincide with their most personal film to date, A Serious Man, the men who famously aren’t there in interviews have decided to put in an appearance. The question, one so obvious it would be murdered in the first act of a Coen brothers’ movie, is why?

A Serious Man comes on the back of the triple Oscar winning thriller No Country For Old Men and the goofball spy comedy Burn After Reading. On the way in 2011 is a remake of True Grit, starring Jeff Bridges in the John Wayne role of Rooster Cogburn.

In that company, A Serious Man (a bleak comedy drama which casts Michael Stuhlbarg as Larry, a modern-day Job) is the real true grit, a life and the universe number that muses on Judaism, the point of existence, the utter randomness of life, and, this being a Coen brothers’ movie, the best way to drain a cyst.

To put it another way, this is a movie that needs to be sold. But there is arguably something more invested in A Serious Man than dollars. Try probing Ethan on that, though. Here come the first of those stray cats.

Why this film, why now? “I don’t know, I don’t know, I don’t know,” he says, then sighs. The younger brother, 52 to Joel’s 55, is sitting at one end of a sofa in a suite at Claridge’s in London, Joel at the other, their jeans, shirts, and generally crumpled air at odds with the room’s exquisitely upholstered formality. Ethan is looking up and out of the window. Joel is looking at me. I’m looking out for cats, big and small. There’s a good cop-vague cop act going on, with Ethan on Academy Award-winning form in the latter role.

There is plenty in A Serious Man to think of it as close to home for the brothers. It is set within a small Jewish community in the Midwest. The Coens were born and brought up in a similar looking suburb, St Louis Park, in Minneapolis. Like the film’s lead character, Larry Gopnik, their parents were academics – father an economics professor, mother an art historian – and around the time the film is set, 1967, they were roughly the same age as Gopnik’s television-obsessed son (and had an older sister who washed her hair a lot).

Like any children, says Joel, they accepted what was around them as the norm. “We had the sense there was our community and there was the larger Gentile community, but we didn’t feel it being in any way peculiar.”

Joel’s wife, the actress Frances ­McDormand, has described it differently. “They grew up pretty isolated as the only Jewish kids around and they’re pretty big on loyalty and ­dependability.”

It is tempting to see the Coens’ career as the story of two filmmakers who started as outsiders and stayed that way. Their very uniqueness is their unique selling point. No other directing, writing and producing duo can match their range or output. From Blood Simple to The Big Lebowski, Barton Fink to O Brother, Where Art Thou, their films have bounced from east coast to west coast, from screwball comedy to crime. While calling to mind past greats from cinema and literature, Alfred Hitchcock and Raymond Chandler among them, the Coens have always put their own unmistakable mark on proceedings. The flying hats in Miller’s Crossing. The peeling wallpaper in Barton Fink. The woodchipper scene in Fargo. In the TV news business if it bleeds it leads. In the Coens’ world, if it’s way out it’s definitely in. Then there is their way of working. Until recently, the director’s credit went to Joel, the producer’s to Ethan, the ­writing credit they shared. Now everything is equal. No wonder they have been dubbed the “two-headed director”.

The closeness seems always to have been there, helped along by a shared love of the box in the corner. “TV was a big part of teenage suburban culture in a way that shocks me now,” says Joel. The nearest cinema was a drive away, meaning most of their movie education came from TV.

“I loved The Wizard Of Oz,” says Joel. “It shared the shit out of me.”

“The Wizard Of Oz is an interesting one,” adds Ethan. “It played every year in the States and our introduction to it was on TV so it was all black and white. No cut to Oz and colour, we totally lost that.”

Joel laughs. “We had no idea part of the movie was in colour!”

This gets Ethan started. “It was all Kansas!”

The ball bounces back to Joel, warming to the memory of that ancient TV set. “Ethan saw Laurence Olivier in Khartoum and then in Othello. He was 25 before he realised that Olivier wasn’t black.”

Ethan snorts with laughter. The two enjoy a joke, one of their favourites being their invention of Roderick Jaynes, film editor of the Hollywood parish. Listed in the credits for Blood Simple as a way of avoiding having their own names appear over and over, Jaynes has hung on through the years, penning a couple of forewords to published screenplays and even winning an Oscar nomination for Fargo.

Blood Simple, released in 1984, was a crucial point in the Coens’ careers. It was their first feature, the point when they put away the Super 8 cameras of childhood and the notions they had at New York University, film school (Joel) and Princeton (Ethan, philosophy), to get started on the real deal of filmmaking. Blood Simple was also where Joel met McDormand, who starred in the picture as a faithless wife.

Crucially, Blood Simple was where the brothers learned a fundamental lesson about filmmaking – that it’s a business. As recounted in Josh Levine’s book, The Coen Brothers: The Story Of Two American Filmmakers, the $750,000 budget for Blood Simple came from small investors they had contacted personally. This wasn’t some grant from an arts organisation, this was cash from people they knew couldn’t afford to lose it. They didn’t. In the US alone, Blood Simple earned back more than three times what it cost to make. It was critically acclaimed, too. Profitable and street credible: the kids from the Midwest were in.

Their next picture, Raising Arizona, ­starring Nicolas Cage and Holly Hunter as a pair of lovable babynappers, was a crowd-pleaser. The Oscar-winning Fargo, a crime caper ­starring McDormand as a Marge even more adorable than Mrs Simpson, and The Big Lebowski, with Jeff Bridges as The Dude, were in the same league: films that you didn’t need to be a Coenista to enjoy. While there were misfires – Intolerable Cruelty with George Clooney and Catherine Zeta Jones, their remake of The Ladykillers – their run of success was remarkable. Then, in 2007, came No Country For Old Men, their most mainstream and multi-garlanded movie.

Cormac McCarthy’s novel could have been written for the brothers, so closely did it chime with their own interest in landscape and how it shapes people. The big skies of Texas in No Country, the wind-blasted tundra in Fargo – setting is a fundamental part of any Coen brothers’ film and to write about a place they need to be familiar with it, to feel it in their bones, however temporarily. It is why their movies take place in America, and why, says Joel, there could never be a Coen brothers’ movie set in Scotland. Well, never say never …

“We did make a short movie once in Paris,” recalls Ethan. “It all took place in a subway station and the main character was an American, which kind of points up the problem. When we think about a story we think about American characters.”

Joel though, who has visited Skye repeatedly on holiday, says he is taken with its “seductive” landscape and relents slightly on the America-only rule.

“I love Scotland, I visit there a lot for the countryside, the landscape of it. I go up to the Isle of Skye. Who knows, maybe some day we will do a movie set in Scotland. It will probably have an American character in it though.”

As Kelly Macdonald proved in No Country, that doesn’t preclude a Scot from taking the role. The brothers have kept in touch with Macdonald since she played Carla Jean Moss, the nervy wife of Josh Brolin’s Llewelyn. Indeed, their fond memories of Macdonald, and my shameless touting of her as a fellow Glaswegian, helped to get the interview off to a warm start (thanks Kelly). Tommy Lee Jones is another actor we turn out to have in common. They directed him in a film that grossed $162 million world-wide. I once waited by the phone for several hours to talk to him, only to be given the brush off. “You dodged a bullet there,” says Ethan. “Not a pleasant fellow,” chips in Joel.

Macdonald can consider herself in with the Coen crowd. Over the course of 14 feature films the brothers can be said to have acquired two sets of families. They live with their ­nearest and dearest in New York: Joel and McDormand have one son, Ethan and his wife, the film editor Tricia Cooke (they met on Miller’s Crossing), have two children. Then there is the other Coen family, the extended clan of actors and actresses who appear in their films – George Clooney, John Goodman, John Turturro, Steve Buscemi, and, of course, McDormand. Add to this crowd the crew members who turn up again and again – including the British director of photography Roger Deakins and set decorator Nancy Haigh.

Beyond these families there are the Coen watchers, fans who have stuck with their movies from the start. Beyond these are the critics. Here, relations have traditionally been trickier. Critics who consider themselves at the serious end tend to regard each new Coen picture like an exam that needs to be passed. Few American filmmakers have been as intellectualised as the Coens, yet it would be hard to find two individuals less willing to play the role of critics’ darlings.

Everything you need to know about the Coens’ practical approach to filmmaking, or the impression they would like you to have, is summed up in two lines from Barton Fink. Barton, a screenwriter newly arrived in ­Hollywood, is stressing over a wrestling picture. “Look, it’s really just a formula,” says an old hand. “You don’t have to type your soul into it.”

Does the theorising bore them stiff? “It does,” says Ethan, and as if to drive the point home he immediately sidesteps into musing about Olivier’s voice in Khartoum.

“Initially we may have been very amused by it but it can get a little bit tedious,” says Joel. “We kind of don’t care. We don’t really mind how people look at the movies, whether it’s in an intellectual way or an emotional way.

It’s not like we think there’s a right or a wrong way.”

The way Ethan explains it, the story is king. Everything – character, dialogue, setting –serves its needs. In that way, just as the rhythm of a good story would be spoiled by interruptions, so the Coens seem to view the analysing of their films as a distraction from the entertainment. Or as one character puts it in A Serious Man: “accept the mystery”.

This is where A Serious Man is revealing, not least in pointing up the difference between the image of the Coens, one they help perpetuate to some extent, and the reality. Here is a picture dealing in the big questions about life by two directors who shun analysis. It’s a picture about relative outsiders, yet it’s made by two filmmakers who couldn’t be any more in the inner circle of Hollywood. With four Oscars, the Coens can do what they want –even remake the iconic western True Grit.

Above all, A Serious Man is a film about the importance of family and community. They have come to a point when they can make the likes of A Serious Man and feel comfortable with what it might reveal about them. Given their obsession with privacy, one suspects that might not be very much. But it is more than before and in that sense this picture signals a coming of age and, as such, it is bound to set the chatter going.

Richard Kind, who plays Uncle Arthur, the character with the cyst, says it is about “how Joel and Ethan Coen view the world and the human condition”. Lest that is a turn off, he adds: “It’s also a good yarn about one very sad SOB”. An SOB, needless to say, that the Coens put through the mill as only they know how. As Ethan says: “The fun of the story for us was inventing new ways to torture Larry. His life just progressively gets worse.”

Facing trouble on the home and work front, Larry does not have his troubles to seek.

Where other men have mild doubts, Larry has moments of terror. Do the Coens ever feel the same, particularly now they are fathers?

“As a father, all the time,” says Joel, laughing. “Parenthood is bewildering sometimes. There’s no question about that.”

And Ethan? Is he a confident person? Here come the last of those stray cats.

“A confident person? Boy. Am I a confident person? Uh, I don’t even know what to say.”

“It’s safe to say Ethan’s a pretty confident person,” says Joel, stepping in and standing up to signal the interview is at an end. “I’m his brother. I’ve known him a long time.”

A Serious Man (15) is on nationwide release.