In a small bowl, combine the warm milk and sugar. Sprinkle the yeast on top and let it sit for about 5 to 10 minutes or until frothy.

In a large mixing bowl, combine the flour and salt. Add the frothy yeast mixture, eggs, melted butter, and vanilla extract. Mix until a soft dough forms.

Dust a clean surface with flour, place the dough on it, and knead for about 5 to 7 minutes until smooth and elastic.

Place the dough in a greased bowl and cover with a kitchen towel. Let it rise in a warm place for about 1 to 1.5 hours or until doubled in size.

Punch down the dough, roll it out to about ½ inch thick, and use a cutter to shape the doughnuts.

Place shaped doughnuts on a lined baking sheet, cover lightly, and let rise for another 30 to 45 minutes.

Heat vegetable oil to 350°F (175°C) and fry the doughnuts in batches until golden brown, about 1 to 2 minutes on each side.

While warm, roll doughnuts in granulated sugar, dip in melted chocolate or fill with jam/custard using a piping bag.