Whisk together flour, sugar, baking powder, and salt.
Mix milk, eggs, melted butter, and vanilla extract in another bowl.
Combine wet and dry ingredients until just mixed.
Roll out the dough on a floured surface to about ½-inch thickness.
Cut out donuts with a donut cutter or two different sized round cutters.
Heat oil in a deep fryer or large pot to 350°F (175°C).
Fry donuts in batches, turning once, until golden brown (about 1-2 minutes per side).
Remove with a slotted spoon and drain on paper towels.
Whisk powdered sugar, milk, and vanilla extract until smooth.
Adjust consistency with more milk or sugar if needed.
Dip cooled donuts in the glaze and let excess drip off.
Place on a wire rack to set.
Serve with coffee or tea. Enjoy!
