Activate the yeast: In a large mixing bowl, combine warm milk, 1 teaspoon of sugar, and active dry yeast. Stir and let sit for 5-10 minutes until foamy.

Prepare the dough: Add remaining sugar, eggs, melted butter, and salt to the yeast mixture. Gradually add flour until a shaggy dough forms. Knead until smooth and elastic.

First rise: Grease a bowl, place dough in it, cover, and let rise for 1-1.5 hours until doubled.

Shape donuts: Roll the dough to 1/2-inch thickness and cut out donuts with a donut cutter. Place on lined baking sheets.

Second rise: Cover shaped donuts and let rise for another 30-45 minutes until puffy.

Prepare frying: Heat oil in a deep pot to 350-360°F.

Fry donuts: Fry 2-3 donuts at a time for 60-90 seconds per side until golden brown. Remove to drain.

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

Glaze and serve: Dip warm donuts in the glaze and let excess drip off. Serve immediately.