It's four years since her antics with a Muppet on a Moped turned a 19-year-old musician from the Czech Republic into a global superstar.
Falling Slowly from Once claimed an Oscar and history was made when the show's host brought Irglova back on stage to allow her to finish her speech. Everyone was embarrassed that her ginger-nutted partner had hogged the limelight.
Undeterred, Irglova contributed to a follow-up Swell Season album that suffered an identity crisis. Two years ago, Irglova and Mister Moped split up as a romantic couple.
Her understated but expertly judged adornments on Liam O Maonlai's album To Be Touched were so flawless they whetted the appetite for a solo album. Full of praise for Irglova, O Maonlai, who walks in the realm of the spirit, won't be disappointed by the 12 tracks on Anar.
For these songs, Irglova has ignored the hectoring, busking aesthetic of her Swell Season sidekick in favour of a delicate examination of the vagaries of love, desire and loss.
Instrumentation is used sparingly, allowing Irglova's piano to carry the musical narrative throughout.
"It's definitely lacking a masculine aspect," says Irglova of the album. "Which is okay."
Not that the artist is devoid of male company or collaborators. She got married earlier this year to studio engineer Tim Iseler in Chicago. Her new hubby co-produces Anar and plays bass and guitar on tracks. His work is subtle. The results, even when the brass and backing vocals swell up on Go Back, the album's poppiest track, never crowd out Irglova's bright tones.
The emotions on Anar are so bare, you feel maybe someone should have warned you that you'd be eavesdropping on a weary spirit reading pages from her tear-stained diary.
Go Back opens with the line, "To know the pain of too much tenderness I'd give myself to thee . . ." and has a pre-Raphaelite quality of a woman trapped in a tower, meditating as she busies herself with embroidery. It's a sonic trompe l'oeil, of course. Irglova is very much a modern woman, unafraid to admit to having deep feelings.
"I tend to write from a more feminine place, like softer," she explains. "I like music that's more soothing and harmonious."
For Old Times Sake carries distant and gentle echoes of Otis Redding's I've Got Dreams To Remember. We Are Good, with it's twinkling guitars, marks the spot where Joni Mitchell's Woodstock meets America's Horse With No Name.
The most contemporary reference point may well be Sufjan Stevens, whose eclectic and playful adventurism reaches far and wide.
So what's this Anar the album's called after? "It means pomegranate (in Persian)," says Irglova. "Pomegranates are really mysterious because they kind of look like not much on the outside and then you open them up and it's this treasure of rubies." She's come a long way from Outspan oranges.