In a large bowl, mix flour, sugar, baking powder, and salt.

Stir in melted butter, milk, egg, and vanilla extract until smooth.

Heat oil in a deep fryer or large pot to 375°F.

Roll out the dough on a floured surface and cut out donuts using a donut cutter.

Fry donuts in batches until golden brown, about 2 minutes per side.

Remove from oil and let drain on paper towels.