Dissolve yeast in warm water. Let sit for 5 minutes.
In a large bowl, combine milk, sugar, salt, butter, and egg. Add yeast mixture.
Gradually add flour, mixing until a soft dough forms.
Knead dough on a floured surface for about 5 minutes.
Place dough in a greased bowl, cover, and let rise until doubled, about 1 hour.
Roll out dough to ½ inch thickness. Cut with a doughnut cutter.
Let doughnuts rise for another 30 minutes.
Heat oil in a deep fryer or large pot to 375°F (190°C).
Fry doughnuts until golden brown, about 1 minute per side.
Drain on paper towels. Dust with powdered sugar or dip in glaze if desired.