Birch received the $25,000 prize for her piece about three generations of women living with mental illness. The premiere production was directed by Katie Mitchell with a cast including Kate O'Flynn and Hattie Morahan.
Of the play's original run, WhatsOnStage critic Sarah Crompton said: "I find it has eaten into my thinking in a way many more conventional plays do not."
Now in its 40th year, the prestigious award is the oldest prize given to female playwrights writing in the English language. This year's finalists – which were chosen from over 150 nominated plays – also included Elinor Cook for Out of Love and Nina Raine for Consent.
Co-founded by Emilie S Kilgore and William Blackburn, previous winners include Sweat by Lynn Nottage and The Flick by Annie Baker, both of which went on to win the Pulitzer Prize for Drama.
This year's panel of judges included Annie Baker, Carrie Cracknell, Denise Gough and Justine Mitchell.