Whisk together flour, sugar, baking powder, and salt in a large bowl. In a separate bowl, combine milk, melted butter, egg, and vanilla extract. Pour the wet ingredients into the dry mixture and stir until just combined. The dough should be slightly sticky but manageable.

Fill a heavy-bottomed pot with 2 inches of vegetable oil and heat to 375°F. Use a candy thermometer for accuracy. The oil should bubble gently when you drop in a small piece of dough.

Using a small cookie scoop or your hands, form the dough into 1-inch balls. Keep them uniform for even cooking.

Carefully drop 6-8 donut holes into the hot oil, being careful not to overcrowd. Fry for 2-3 minutes until golden brown, turning once halfway through. Remove with a slotted spoon and drain on paper towels.

Mix cinnamon and sugar in a shallow bowl. While donut holes are still warm, brush with melted butter and roll in the cinnamon sugar mixture.