Combine the flour, sugar, baking powder, and salt in a large mixing bowl.
In another bowl, whisk together the milk, eggs, melted butter, and vanilla extract.
Slowly incorporate the wet ingredients into the dry ingredients, mixing until a soft dough forms.
Roll out the dough on a floured surface and cut out donut shapes using a donut cutter or round cookie cutters.
Heat the vegetable oil in a deep fryer or pan to 350°F (175°C).
Carefully fry the donuts until they are golden brown, turning them once to ensure even cooking.
Remove the donuts with a slotted spoon and place them on paper towels to drain excess oil.