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

In a separate bowl, combine warm milk, egg, and melted butter. Add the wet ingredients to the dry ingredients and mix until a soft dough forms.

Knead the dough on a lightly floured surface for 5-7 minutes until smooth and elastic, then cover the bowl with plastic wrap and let it rise in a warm place for about 30 minutes, or until doubled in size.

Once risen, gently punch down the dough and roll it out to about 1/2-inch thickness. Use a small round cutter or knife to cut out doughnut holes.

Heat vegetable oil in a large pot or deep fryer to 350°F (175°C). Carefully drop the doughnut holes into the hot oil, frying them in batches for 2-3 minutes per side, until golden brown.

Remove the doughnut holes with a slotted spoon and place them on a wire rack lined with paper towels to drain excess oil. Immediately toss them in a bowl with your desired coating, such as cinnamon sugar or powdered sugar, while still warm.