Activate the yeast:

• In a large bowl, combine warm milk, yeast, and a pinch of sugar. Let sit for 5–10 minutes until foamy.

Make the dough:

• Add the sugar, eggs, melted butter, and vanilla to the yeast mixture. Stir to combine.

• Mix in the flour and salt until a dough forms.

• Knead by hand or with a stand mixer for 5–7 minutes until smooth and elastic.

• Place the dough in a greased bowl, cover, and let rise in a warm place for 1–1½ hours, or until doubled in size.

Shape the doughnuts:

• Punch down the dough and roll it out on a floured surface to about ½-inch thickness.

• Use a doughnut cutter or two round cutters to cut out doughnuts and holes.

• Place on a floured baking sheet, cover lightly, and let rise for another 30–45 minutes.

Fry the doughnuts:

• Heat 2–3 inches of oil in a deep pot to 350°F (175°C).

• Fry 2–3 doughnuts at a time for 1 minute per side, or until golden brown.

• Remove and drain on paper towels or a wire rack.

Make the glaze:

• In a bowl, whisk powdered sugar, milk, and vanilla until smooth.

Glaze the doughnuts:

• Dip each warm doughnut into the glaze, let the excess drip off, then place on a wire rack to set.