In the bowl of a stand mixer or a large mixing bowl, cream the softened butter, granulated sugar, and light brown sugar together on medium speed until light and fluffy, about 2-3 minutes. Add the egg yolks one at a time, beating well after each addition. Stir in the vanilla extract and sour cream until fully incorporated.

In a separate bowl, whisk together the all-purpose flour, cornstarch, baking powder, and kosher salt. Gradually add the dry ingredients to the wet ingredients in three increments, mixing just until combined. The dough will be thick and slightly sticky. Cover the bowl with plastic wrap and refrigerate for at least 1 hour.

Fill a Dutch oven or heavy-bottomed pot with approximately 3 inches of vegetable oil (about 7 cups). Heat the oil over medium-high heat until it reaches 350°F (175°C). Use a thermometer to ensure consistent frying temperature.

Lightly flour a clean work surface and a rolling pin. Turn the chilled dough onto the surface and roll it out to 1/2-inch thickness. Use a floured donut cutter or two round cutters (approximately 3 inches and 1 inch in diameter) to cut out the donuts. Gather the scraps, re-roll the dough once, and cut out additional donuts. The remaining dough can be used to make donut holes.

Fry 3-4 donuts at a time in the hot oil, flipping halfway through, for 2-3 minutes total or until golden brown. Remove the donuts with a slotted spoon and place them on a wire rack lined with paper towels to drain excess oil. Repeat with the remaining donuts and donut holes, frying the holes for about 1-2 minutes.

In a medium bowl, whisk together the powdered sugar, milk, and vanilla extract until smooth. Adjust the consistency if necessary by adding more milk for a thinner glaze or more powdered sugar for a thicker coating.

Dip each slightly cooled donut into the glaze, ensuring both sides are coated. Use a fork or your fingers to flip the donut, allowing excess glaze to drip off before placing it back on the wire rack. Let the glaze set before serving.