Natalie Prass has attracted all sorts of epithets recently.

For Rolling Stone magazine, she is one of Ten New Artists You Need to Know, while Time included her in their list of 15 Artists to Watch in 2015. The woman in question, however, opts for a less exalted job description. "I'm this crazy maniac travelling person," she laughs. "Basically, my calendar has blown up."

The 29-year-old Virginian has been in constant motion since the release of her self-titled debut album at the beginning of the year. Before that, she was playing keyboards and singing backing vocals on tour with Jenny Lewis. "I've been on the road for two years and it's overwhelming," she says the morning after a gig in Madrid, caught somewhere between exhaustion and gratitude. After ten years of trying, success is "life-changing, but I feel like I've earned it".

Prass's eponymous debut album is, simply, one of the best records released in the first half of 2015. A sumptuous Southern soul classic-in-waiting, it marries her stunning voice and songs of hurt and heartbreak to lush, old school production values, replete with horns and strings. The album has picked up numerous critical garlands, but getting to this point wasn't easy, not least because Prass has never been willing to take shortcuts.

"Long story short, I'm super stubborn," she says. Before joining Lewis's band, Prass had struggled for several years in Nashville, where she'd moved in her early 20s. By day she worked in a friend's coffee shop and "designed clothes for dogs". By night she wrote songs, played shows, and plotted her path. "I got offered publishing deals to write country music, but it was not what I wanted to do," she says. "I turned down a lot of stuff. I'm in my 20s, and I thought, this is my time to experiment and be me. I was poor. I struggled big time, living hand to mouth so I could be the kind of artist I want to be. I'm pretty picky about what I do and who I work with, for better or for worse."

For a long time, Prass's timeless tastes seemed at odds with the prevailing trend for "soulless" mainstream country and minimalist electronic duos. "I was having meetings, going to bars, talking to people in Nashville about music," she recalls. "This was 2011. When I said, 'Brill Building, Dionne Warwick, Burt Bacharach, Stephen Sondheim', people were like, 'What? You're trying to get strings and horns, are you crazy?'"

Perhaps unsurprisingly, her breakthrough came not in Nashville, but with a serendipitous reconnection with Matthew E White, a childhood acquaintance from back home in Virginia. The brains behind Spacebomb, a bespoke studio, label and production stable located in Richmond, White has since released two highly acclaimed albums, 2012's Big Inner and this year's Fresh Blood. At the time, however, he was operating under the radar.

"Matt and I first met when we were really young in Virginia Beach, although we weren't really friends because he's a little bit older than me," says Prass. They were both serious about making music but had lost touch, until by chance a Nashville friend played Prass an album he was working on, adding that it had been produced by "this guy called Matthew E White from Richmond. I was like, 'What, Matt? I know him!' I had no idea that he could produce, or arrange horns. I just knew him as this jazzy, folk guitar-player dork." She cracks up. "Don't get me wrong, I'd always really admired him. I thought he was the coolest person, but he was still a music nerd like me.

"This music sounded so good, so I reached out to him and we clicked. It was really natural, and now we're so close. Not only do we love the same kind of music, we grew up around the same scene in Virginia Beach, and I feel like that has a lot to do with our connection. It just made so much sense, it was almost like fate."

The resulting album, written by Prass and produced by White and his Spacebomb partner Trey Pollard, draws on classic country-soul, R&B and orchestral pop. Among the overt echoes of Dusty Springfield, Dionne Warwick and Isaac Hayes, there are hints of the cool, modern feel of fellow Virginia Beach natives Pharrell Williams and Timbaland. This is no retro retread. "As much as we respect and have learned a lot from the people before us, we're not trying to make replica music," says Prass. "We're trying to make something new, that's really important to me. Learn from other people, of course, but at the end of the day it's my sound and my voice."

It's also her story. Like many classic soul records, the record mines a mood of exquisite melancholy, half in love with the heartache it so luxuriantly describes. Opener My Baby Don't Understand Me, on which Prass sings "our love is like a long goodbye", firmly establishes the primary theme. The songs are autobiographical, she concedes, although she's been singing them so long the feelings which inspired them are no longer raw. "I don't think about who they're about and when I actually wrote them anymore," she says. "I think about new experiences and apply them to those."

Though it was only released this year, Prass recorded her debut in 2013, and is already looking towards the next record. "I have a lot of new songs, my head is full of ideas," she says. "I'm not dying to get them out there yet, though. It's still a little scary, getting the songs ready and putting it all together. I'm one of those people who don't want to share anything till it's a done deal." Will she be working with White on the next album? "Everyone is so busy, and I don't want to overwhelm him, but I'd love him to be involved in any way he can be involved."

In the meantime, her remarkable debut album continues picking up momentum. Fresh from an appearance on Later... with Jools Holland in April and a UK tour supporting Ryan Adams, Prass is back in Britain for her own headlining dates, including a Glasgow show with her three-piece band. It has, I suggest, already been quite a year. "I know," she reflects. "When you're living it, you can forget what's happening. I have to keep reminding myself that this is so exciting."

Natalie Prass is out now, released by Spacebomb. She plays Mono, Glasgow, on June 22