In a stand mixer add the butter and sugar, beat until well combined. Add the egg yolks, salt, and vanilla extract, mixing until well combined. Mix in the sourdough starter and the beer.

Stop the mixer, sprinkle with flour, cornstarch, and baking powder, mix until just combined (don’t over mix or your doughnuts will be tough) dough will be soft and slightly sticky.

Lay down a long sheet of plastic wrap, scoop all the dough into the center of the plastic wrap and fold the plastic around the dough until well-sealed. Refrigerate until chilled, at least 1 hour and up to 3 days.

Roll the dough out into a 1/3 inch thickness on a well-floured surface, sprinkle the top with more flour before rolling. Cut out 3-inch circles, then cut a 1-inch circle hole in the center.

Add to a baking sheet covered with parchment paper, brushing the excess flour off the doughnuts.

Chill the doughnuts while the oil heats or for at least 30 minutes.

Heat 3-5 inches of oil in a deep fryer or a pot with a deep-fry thermometer clipped on the side until it reaches 325°F.

Prick the doughnuts lightly on the top with a fork a few times. A few at a time fry the doughnuts on each side until golden brown. Remove from oil and allow to cool on a stack of paper towels.

Mix all the glaze ingredients together in a wide shallow bowl with a fork until well combined and free of lumps.

Dip the doughnuts into the glaze until covered on both sides, add a place on a stack of paper towels or a wire rack over a baking sheet until set.