With an electric mixer, cream together softened butter and sugar. Add egg, vanilla, and milk. Stir in baking powder, salt, and flour with a spoon until combined. **Do not over mix or your donut holes will become dense.**
Grease a mini muffin tin and fill each spot with batter 2/3 of the way full. Bake for 10 minutes at 400°, or until the edges become a light brown. Remove from the oven and set aside to cool.
Place melted butter and powdered sugar in separate bowls. Dunk each donut hole completely into the butter then place in the powdered sugar bowl and coat. Set on a cooling rack for the coating to dry.