A few years back, around 2010 or so, Natasha Khan stayed at Beck's house for a few weeks, using his studio and recording demos. She has said it was very useful for breaking her writer's block. She then took her recordings and went and finished her album without him. Beck only real work on that album, The Haunted Man
, was the song "Marilyn."
Also of course, they had collaborated on the track "Let's Get Lost" for the Twilight movie, though I am not certain if it was a product of that visit (I believe it came first).
Anyway, then in 2014, Natasha Khan made a little short film, under two minutes long, called "Under The Indigo Moon." The soundtrack is a song of the same name, which is credited as a collaboration with Beck. In talking about the song, she mentions her visit to Beck's studio, but it's not clear if this "Under The Indigo Moon" is a product of back then, or a newer collaboration.
Also the song in the film is just a snippet, not the entirety of the song.
You can watch her video here:
Natasha Khan: Under the Indigo Moon on Nowness.com