Activate the Yeast: In a small bowl, dissolve the yeast in warm water. Let it sit for 5–10 minutes until foamy.

Make the Dough: In a large bowl, mix the milk, sugar, salt, butter, and egg. Stir in the yeast mixture. Gradually add the flour, mixing until a soft dough forms.

Knead and Rise: Knead the dough on a floured surface for about 5 minutes until smooth. Place it in a greased bowl, cover, and let rise in a warm spot for 1 hour or until doubled in size.

Cut the Doughnuts: Roll the dough to about 1/2-inch thick. Use a doughnut cutter or two round cutters to shape the doughnuts and holes. Place on a floured tray, cover lightly, and let rise again for 30–45 minutes.

Fry: Heat oil in a large pot or deep fryer to 350°F (175°C). Carefully drop in doughnuts a few at a time. Fry for 1–2 minutes per side or until golden. Drain on paper towels.

Make the Glaze: Whisk powdered sugar, milk, and vanilla until smooth.

Dip and Serve: While the doughnuts are still warm, dip each one into the glaze and place on a wire rack to let the excess drip off. Enjoy warm or let the glaze set.