Froth the yeast. In a large measuring cup, combine the warm milk, dry active yeast, and 2 tablespoons of sugar. Whisk them together and let the mixture froth for 5-10 minutes.
Combine dough ingredients. In a stand mixer, add the flour, rest of the sugar, salt, butter, egg and egg yolks, vanilla, and yeast mixture. Begin mixing the donut dough with the hook attachment at low speed.
Mix the dough. Once there are no more dry patches of flour, bring the speed up to high and continue mixing for 10-15 minutes. The dough should be a little sticky and tacky to the touch.
Let the dough rise. Grease a large bowl (I used about 1-2 teaspoons of olive oil) and place the dough in it. Cover it with plastic wrap and let it rise for 1-2 hours, or until it doubles or even triples in size.
Roll out the dough. Once the dough has finished rising, punch it down and place it on a floured surface. Roll it out with a rolling pin to about 1/2-inch thick.
Cut out donut circles. Using a 3-inch biscuit cutter or glass cup, cut out circles in the dough. Once you’ve cut out as many as you can, reshape and roll out the scraps, and then cut out more circles. You should get about 16 sugar donuts in total.
Let them rise again. Place the cut-out donuts on a parchment paper-lined baking sheet and cover it with a thin kitchen towel or plastic wrap. Let them rise for 30 minutes.
Fry the donuts. In a heavy-bottomed pot, heat 2 inches of corn oil to 340 degrees Fahrenheit. Fry each donut for about 2 minutes per side, until golden brown. Then use a large slotted spoon to transfer the donuts to a baking sheet lined with paper towels.
Cover the donuts in sugar. Once the donuts have cooled and are only warm now, roll them in a bowl with 1 cup of granulated sugar. Then serve and enjoy these perfect sugar donuts.