Last year, the shambling, quizzical, brilliant Australian singer-songwriter Courtney Barnett collected a bunch of her music into The Double EP: A Sea Of Split Peas. She insisted it wasn’t her debut album, but we gave it Album Of The Week anyway. Barnett played both Coachella weekends, despite Coachella maybe not being the best environment for sharply-written stoner fantasias. And last night, she showed up on American TV for the first time ever as the musical guest on The Tonight Show, where she played “Avant Gardener,” her amazing story-song about a midday medical emergency. Watch her exceedingly winning performance below.

The Double EP: A Sea Of Split Peas is out now on Mom + Pop, and check out the great Grantland feature that my friend Sean Fennessey wrote about Barnett at Coachella. Sean should write about music more.