Warm the milk in a pot.
Dissolve the yeast in the warm milk.
Mix sugar, salt, and flour together.
Add the yeast mixture, eggs, and butter.
Knead the dough until smooth and elastic.
Cover and let it rise until doubled.
Roll out the dough on a floured surface.
Cut out donuts with a donut cutter.
Save the donut holes.
Heat vegetable oil in a deep pan.
Fry donuts until golden brown.
Drain on paper towels.
Using a bowl, combine milk and powdered sugar.
Add vanilla extract for flavor.
Stir until smooth and pourable. Pour glaze on each donut and enjoy!