Instructions:

In a mixing bowl, combine warm milk, sugar, and yeast. Allow it to sit for 5 minutes until it becomes frothy.

Add beaten egg, melted butter, and vanilla to the mixture. Gradually incorporate the flour to form a soft dough.

Knead the dough on a floured surface until smooth. Place it in a greased bowl, cover, and let it rise for 1 hour.

Roll out the dough to a 1/2-inch thickness. Cut out doughnuts using a doughnut cutter.

Heat oil in a deep fryer or large pot to 375°F (190°C).

Fry the doughnuts in batches until they turn golden brown. Drain them on paper towels.

For the glaze, whisk together powdered sugar, milk, and vanilla until smooth.

Dip each doughnut into the glaze and let them set on a wire rack.