Knead:
Turn the dough out onto a floured surface and knead until smooth and elastic.
First Rise: Place dough in a greased bowl, cover, and let rise in a warm place until doubled in size, about 1 hour.
Shape Donuts: Roll out the dough to about 1/2 inch thickness. Cut out donuts with a donut cutter or round cookie cutter and a smaller cutter for the holes.
Second Rise: Place shaped donuts on a floured surface, cover, and let rise until puffed up, about 30 minutes.
Fry: Heat vegetable oil in a deep fryer or large pot to 350°F (175°C). Fry donuts in batches until golden brown on each side. Remove and drain on paper towels.
Glaze: Mix powdered sugar, milk, and vanilla extract to make the glaze. Dip or drizzle over warm donuts.
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