In a bowl of a mixer whisk together the active sourdough starter, water, butter, egg yolks, and vanilla.
When the doughnuts have doubled, fry a few at a time trying not to overcrowd the pot. Fry for 45 seconds until they just start to get golden brown. (the doughnuts will darken even more as they cool). Flip each doughnut and fry for an additional 45 seconds.