Gather ingredients: flour, sugar, yeast, milk, eggs, butter, salt, oil, and optional vanilla or nutmeg
Warm the milk until lukewarm
Mix warm milk, yeast, and a little sugar
Let the yeast sit until foamy
Add eggs, melted butter, sugar, salt, and flavoring
Mix in flour until a soft dough forms
Knead the dough until smooth and elastic
Place the dough in a greased bowl
Cover and let it rise until doubled in size
Roll out the dough on a floured surface
Cut into donut shapes
Place the cut donuts on a tray and let them rise again
Heat oil in a deep pan or fryer
Fry the donuts until golden on both sides
Remove and drain on paper towels
Add glaze, sugar, or icing if desired
Serve warm or at room temperature