Step 1: Activate the Yeast : Warm the milk until it’s just lukewarm. Add the yeast and 1 teaspoon of sugar to the milk. Stir lightly and let it sit for 5–10 minutes, until frothy and bubbly.

Step 2: Prepare the Dough : In a large mixing bowl, whisk together the remaining sugar, melted butter, egg, and salt. Add the activated yeast mixture and stir until combined. Gradually mix in the flour, one cup at a time, until a soft dough forms. Turn the dough onto a lightly floured surface and knead for about 5–7 minutes, until smooth and elastic.

Step 3: First Rise : Place the dough in a lightly greased bowl, cover with a clean towel or plastic wrap, and let it rise in a warm place for 1 hour, or until doubled in size.

Step 4: Shape the Donuts : Once risen, punch down the dough to release air. Roll out the dough to about 1/2 inch thick. Cut out donuts using a 3-inch donut cutter (or use a large round cutter and a small one for the center hole). Transfer donuts to a parchment-lined baking sheet, cover, and let rise again for 30 minutes.

Step 5: Fry the Donuts : Heat oil in a large, deep pot to 350°F (175°C). Carefully drop 2–3 donuts at a time into the oil, frying for 45–60 seconds per side, or until golden brown. Remove and drain on a wire rack or paper towels.

Step 6: Make the Vanilla Glaze : In a medium bowl, whisk powdered sugar, milk, vanilla extract, and salt until smooth and glossy. If the glaze is too thick, add a few drops of milk; if too thin, add more sugar.

Step 7: Glaze the Donuts : While the donuts are still warm, dip the tops into the glaze. Place them on a wire rack (with a tray underneath to catch drips). Let the glaze set for 10–15 minutes before serving.