In a mixing bowl, whisk together the flour, sugar, baking powder, and salt.

In another bowl, beat the egg, then add milk, melted butter, and vanilla extract. Mix well.

Combine the wet ingredients with the dry ingredients and mix until just combined.

Roll out the dough on a floured surface to about 1/2 inch thick.

Use a cookie cutter to cut out doughnut shapes.

Heat the vegetable oil in a frying pan over medium heat. Fry the doughnuts until golden brown, about 2-3 minutes on each side.

Remove from oil and drain on paper towels.

Dust the warm doughnuts with powdered sugar and cinnamon if desired.

Serve immediately and enjoy!