In a large measuring cup, combine 1 cup of warm whole milk, 2½ tsp dry active yeast, and 2 tablespoons granulated sugar. Whisk well and let rest for 5-10 minutes until frothy.

In the bowl of a stand mixer, add 3 1/2 cups all-purpose flour, 1/2 cup granulated sugar, 1/2 teaspoon salt, 3 tablespoons room temperature unsalted butter, 1 large egg, 2 large egg yolks, and 1/2 teaspoon vanilla extract.

Pour in the frothy yeast mixture from step 1.

Attach the dough hook and mix on low speed until no dry patches remain.

Increase speed to high and knead for 10-15 minutes until the dough is slightly sticky.

Transfer dough into a greased bowl, cover with plastic wrap, and let rise in a warm place for 1-2 hours or until doubled in size.

Punch down the risen dough and turn it onto a floured surface. Roll to 1/2 inch thickness.

Cut out donut shapes using a 3-inch cutter. Re-roll scraps for about 16 donuts total.

Arrange shaped donuts on a parchment-lined baking sheet. Cover and let rise for another 30 minutes.

Heat corn oil in a heavy pot to 340°F. Use an instant-read thermometer.

Fry donuts in batches for about 2 minutes per side, until golden brown.

Remove donuts with a slotted spoon and drain on paper towels.

While warm but not hot, roll each donut in granulated sugar until fully coated.