In a medium bowl, dissolve 2 tablespoons of yeast into ¾ cup of milk. Add ¾ cup of flour and stir to create a smooth paste. Cover the flour mixture and let rest in a warm spot for 30 minutes.

Combine ¼ cup of room-temperature milk and 1 tablespoon of yeast in the bowl of a stand mixer fitted with the paddle attachment. Add the rested flour mixture, sugar, salt, vanilla, and egg yolks. Mix until smooth.

Turn off the mixer and add ½ cup of the remaining flour. Mix on low for about 30 seconds. Add the butter and mix until incorporated, about 30 seconds.

Switch to a dough hook and add more flour, about ¼ cup at a time with the mixer turned off, kneading the dough at medium speed between additions until it pulls completely away from the sides of the bowl and is smooth and not too sticky.

Cover the bowl with plastic wrap and refrigerate for at least 1 hour (and up to 12 hours).

20 minutes before taking the dough out, heat a heavy-bottomed pot with at least 2 inches of oil until a deep-fat / candy thermometer registers 360ºF.

Line a baking sheet with a lightly floured non-terry dish towel. Roll out the dough on a slightly floured surface to ½ inch thick. Cut out 3-inch-diameter rounds with 1-inch-diameter holes.

Place the doughnuts on the baking sheet at least 1 inch apart and cover with plastic wrap. Let sit in a warm spot to proof until they almost double in size, 5 to 20 minutes, testing at five-minute intervals.

Once the doughnuts have proofed, carefully place the doughnuts in the oil. Fry for 1 to 2 minutes per side, or until golden brown.

Remove with a slotted spoon, drain on a wire rack over a paper towel, and let cool before glazing.

Prepare the glaze, recipes follow.

Glaze the doughnuts, cover them with sprinkles, cover the doughnuts in powdered sugar, or a mix of each. Enjoy!