In a large bowl, combine warm milk, active dry yeast, and a pinch of sugar; let it bloom for 5-10 minutes until foamy.

Whisk in remaining sugar, eggs, melted butter, and salt into the yeast mixture, then gradually add flour until a soft dough forms.

Knead the dough on a floured surface for 5-7 minutes until smooth and elastic, then place it in a greased bowl, cover, and let rise in a warm place for 1-1.5 hours until doubled.

Gently punch down the risen dough, then roll it out to about 1/2-inch thickness on a floured surface and cut out donut shapes using a donut cutter or two different sized round cutters.

Place cut donuts on parchment-lined baking sheets, cover lightly, and let rise again for 30-45 minutes until visibly puffy.

Heat vegetable oil in a deep fryer or heavy-bottomed pot to 350-375°F (175-190°C); carefully fry donuts 2-3 at a time for 1-2 minutes per side until golden brown.

Remove fried donuts with a slotted spoon and place them on a wire rack set over paper towels to drain excess oil, then cool slightly before glazing or dusting.

For a simple glaze, whisk together powdered sugar, a little milk, and vanilla extract until smooth, then dip cooled donuts into the glaze or dust with powdered sugar.