In a small bowl, dissolve the yeast and 1/2 teaspoon sugar in warm water. Let stand until frothy, about 5 minutes.
In a large mixing bowl, combine flour, 2 tablespoons sugar, and salt. Add in the yeast mixture, warm milk, butter, and egg yolks. Mix until a soft dough forms.
On a floured surface, knead the dough until smooth and elastic, about 6-8 minutes. Place in a greased bowl, cover, and let rise in a warm place until doubled, about 1 hour.
Punch down the dough and roll out to 1/2 inch thickness on a floured surface. Cut with a donut cutter or use a round cutter and make holes with a smaller cutter.
Place cut donuts on a baking sheet, cover with a clean towel, and let rise until puffy, about 30 minutes.
Heat oil in a deep fryer or large pot to 375°F. Fry donuts in batches until golden brown, about 1 minute per side. Drain on paper towels.
While still warm, roll donuts in sugar to coat. Serve warm or at room temperature.