Iain Cook must be doing something right.

Last year he produced my No 1 Scottish Album of the Year, Traces by Karine Polwart. This year he goes one better with a dominant hand in the playing, writing and production of my latest No 1 Scottish Album of the Year: The Bones Of What You Believe, by Chvrches. Reach back to 2010, before I'd decided to enshrine an end-of-year poll in print, and Cook would have featured on yet another No 1 Scottish Album of the Year: the debut release by The Unwinding Hours. I'm fairly partial to his former band, Aereogramme, too…

The last time I interviewed him, he was with Craig B, the other half of The Unwinding Hours, in a pub opposite Kelvingrove Art Gallery and Museum, and we were talking about the low-key release of their band's second album, Afterlives. This time, when we talk about Chvrches, he's on his mobile in a café in Seattle. "We're going to do Letterman next week," he says down the line. It's hard to believe these two conversations take place only 16 months apart.

It's been an unprecedented year for Chvrches, the three-piece consisting of Cook, Martin Doherty and Lauren Mayberry. The first sign that something meteoric might happen was when they appeared in fifth position on the BBC's influential Sound Of 2013 poll almost exactly a year ago.

Even that, however, didn't hint that The Bones Of What You Believe would go Top 10 in the UK, Top 20 in Australia and Ireland, Top 30 in Germany and Norway. Most impressive of all was the Billboard 200 chart in the US: the album entered at No 12, ahead of Sting's latest and, that first week, sold more than Keith Urban, Avicii and Robin Thicke.

"We just couldn't believe it," Cook laughs. "To get a Top 20 album in America … I don't think it was even on our radar of expectations. The response from the American audiences and radio stations has been absolutely unbelievable."

As if to emphasise the band's Stateside success, he tells me about the gig they're playing later that day (sandwiched between coast-to-coast jaunts to do Jimmy Kimmel's TV show one week, that date with David Letterman the next). It's called the Deck The Halls Ball, curated by a big American radio station, and Chvrches will be sharing the bill with Arctic Monkeys, Vampire Weekend, Phoenix and Lorde.

"Just being allowed to play on the same stage as these people is an incredible thing," he admits. "But I have to treat it as if it's just another day, because otherwise I would freak out. When you play Jimmy Kimmel, you can't think how many people are actually watching; you've just got to play to the people in the room and treat it as a normal gig."

Even after years of touring, particularly with Aereogramme, the Chvrches phenomenon is something else entirely for Cook. "I've never had an experience that's been quite as mental as this, in terms of how fast things have moved… When we were in Japan earlier this year, we had two full eight-hour days of interviews, TV shows and stuff. That's exhausting. Before all this, maybe you weren't travelling in comfort and were sitting in the back of a van for six hours or whatever, but the only thing you had to think about was showing up at the venue, soundchecking and performing. It's just a different kind of daily schedule. I'm not complaining - it's absolutely brilliant - but it's hard work."

The fact that the album is so good makes Chvrches's world domination all the sweeter. The Bones Of What You Believe has an addictive modern synth-pop surface, with all those fantastic tunes that glide across the radio airwaves.

But beneath that, there's something much more musically intelligent going on: there are references here to everything from post-punk inventiveness to warehouse rave, from 1980s John Carpenter-style horror movie soundtracks to the kind of post-rock epic tension that Aereogramme excelled at. It's a rare thing: a global pop hit with enduring substance.

I ask Cook what's the achievement he's proudest of in this whirlwind year. "The fact that we made the album in the same place that we started: a wee basement studio in Glasgow where I worked with Karine, where I worked with The Unwinding Hours, and did a bunch of TV stuff and produced loads of other bands. We didn't take it away to a posh studio or go to LA; we kept it in that little basement studio surrounded by a bunch of keyboards and computers and stuff. That's the thing that I'm proudest of: that we were able to make an album that has had international recognition with the very limited means we had at our disposal."

Chvrches have one last blowout left for 2013, when they take to the stage as part of Edinburgh's Hogmanay line-up. "I've actually never been to Edinburgh at Hogmanay," Cook admits. "I tend to stay in at the New Year, so it might be a shock to the system. No Jackie Bird on the TV! The thing that really clinched it for me, aside from being a great opportunity for the band, was that I'd get to see the Pet Shop Boys play live in Princes Street Gardens with their incredible show. I'm really excited about that."

Who's to say that Neil Tennant and Chris Lowe won't be keeping an eye on Chvrches' set and taking some notes too?