Warm milk to 110°F and stir in yeast. Let sit 5 minutes until foamy.
Mix in sugar, salt, eggs, and melted butter until combined.
Gradually add flour, mixing until dough pulls away from bowl sides.
Knead 5-7 minutes until smooth and elastic.
Place dough in a greased bowl, cover, and let rise 1 hour until doubled.
Roll out dough to ½-inch thickness, cut into shapes, and let rise 30 minutes.
Heat oil to 375°F. Fry doughnuts 1 minute per side until golden.
Drain on paper towels, then glaze or fill as desired.