1. In a large bowl combine ½ teaspoon of the dry yeast with ½ cup lukewarm water. Let stand for 5 to 10 minutes until the yeast foams, then stir in 2½ cups of the flour. Cover with plastic wrap and put in a warm place for at least 45 minutes, or until the dough has doubled in size.

2. In the bowl of a standing electric mixer, combine the remaining 2½ cups flour, sugar, salt, and the remaining ½ teaspoon yeast. Stir to combine well.

3. Using the paddle attachment on slow speed, beat in the warm milk and melted butter. Add the egg yolks one at a time, beating until the dough is smooth and homogeneous. Cover with plastic wrap and let stand in a warm place for 45 minutes.

4. Using the electric mixer, combine the two doughs into one. Break off a piece of dough about the size of a softball and roll it out ¼-inch thick on a clean, floured work surface. Cut out doughnut rounds using a 2-inch cookie cutter. Place the rounds on a baking sheet with plenty of room in between, about 15 per sheet. Repeat until all the dough has been cut. Let the rounds rest for at least 15 to 20 minutes, or until they have tripled in size.

5. Pour enough vegetable oil into a deep fryer or stockpot to measure at least 3 inches. Heat to 325° F on a deep-fat thermometer. Fry the doughnuts in batches, about 5 to 10 minutes per batch, until they are golden brown and very puffy. Drain on paper towels and keep in a warm place until all doughnuts are cooked. Toss the doughnuts in sugar while still warm and serve.