1. In a bowl, whisk together the flour, sugar, baking powder, and salt.
2. In another bowl, mix together the milk, egg, melted butter, and vanilla extract.
3. Combine the wet and dry ingredients until just combined. Be careful not to overmix.
4. Heat oil in a pot or deep fryer to 350°F (175°C).
5. Using a mini donut pan or a piping bag, carefully pipe small circles of batter into the hot oil.
6. Fry the mini donuts for about 1-2 minutes on each side, until golden brown.
7. Remove the mini donuts from the oil and drain on paper towels.
8. Optionally, toss the warm donuts in cinnamon sugar or powdered sugar.
9. Enjoy your delicious homemade mini donuts!