In a small bowl, mix warm milk and yeast. Let sit for 5-10 minutes until foamy.
In a stand mixer bowl, combine flour, sugar, and salt. Add the yeast mixture, egg yolks, butter, and vanilla.
Mix using the dough hook until a soft dough forms, about 5 minutes.
Cover and let rise in a warm spot until doubled, about 1-2 hours.
Roll the dough to 1/2 inch thick and cut into rounds. Let them rise again for 30 minutes.
Heat oil in a deep pot to 350°F (175°C). Fry doughnuts in batches until golden brown, about 2 minutes per side.
Drain on paper towels, then roll in granulated sugar.
If filling, use a piping bag to fill with jam, custard, or chocolate spread. Serve warm!