In a large mixing bowl, whisk together the flour, sugar, salt, and yeast.

Add the warm milk, egg, and melted butter to the dry ingredients. Stir until a dough forms.

Turn the dough onto a floured surface and knead for about 5-7 minutes.

Place the dough in a greased bowl, cover it with a towel, and let it rise in a warm area for about 1 hour.

Punch down the risen dough and turn it out onto a floured surface. Roll it out to about 1/2 inch thick.

Use a round cutter to cut out circles from the dough.

Place the cut-out doughnuts on a floured baking sheet, cover, and let them rise for another 30 minutes.

Heat oil in a frying pan to 350°F and fry the doughnuts in batches until golden brown on each side, about 2-3 minutes per side.