Make the glaze: In a small bowl, whisk together powdered sugar, milk, and vanilla extract until smooth. Set aside.

Heat the oil: Pour 2-3 inches of oil into a large heavy-bottomed pot. Heat over medium-high until the temperature reaches 345°-355°F (about 15-20 minutes).

Prep the cooling area: Set a cooling rack on top of a rimmed baking sheet. Set aside.

Mix wet ingredients: In a liquid measuring cup, whisk together the milk, egg, and vanilla extract. Slowly pour in the melted butter while whisking. Small solid butter beads may form - this is normal and helps with fluffy texture.

Mix dry ingredients: In a large mixing bowl, whisk together flour, sugar, baking powder, and salt.

Combine: Pour the wet mixture into the dry ingredients and stir until a soft dough forms.

Fry the dough: Once the oil is ready, use a small cookie scoop to carefully drop 1 tablespoon-sized scoops of dough into the hot oil. Fry 5-7 at a time, cooking about 1 minute per side until golden brown.

Cool: Use a slotted spoon to remove donut holes and place them on the prepared rack. Let cool for 10 minutes.

Glaze: Dip each donut hole into the glaze, let excess drip off, then return to the rack to set.

Serve: Enjoy warm with coffee or cold milk.