Make your glaze by combining the milk and powdered sugar in a small bowl. Set aside. Pour out another bowl of powdered sugar.
Prep for frying. Put paper towel on a wire rack near the stovetop.
Start by pouring the oil into a medium saucepan: at least two inches of oil. Begin to heat - aim for 350℉ (this will be a low/medium heat).
Make the donut dough by combining the flour, baking powder and sugar. Then whisk in the egg, melted butter and milk. The batter should be thick.
Use a cookie scoop or similar to place balls of dough into the saucepan of oil. Do about 3-4 at a time to avoid overcrowding. Start with one to check the oil is hot enough that the outside is frying, and that when it's done, the inside is fully cooked.
Fry the donuts in batches, scooping tablespoons of dough and flipping when the base looks golden (about 2 minutes total time).
Remove with a slotted spoon and place on the paper towels.
Once all are fried, begin to dip them into the glaze or powdered sugar. Set on a wire rack to drip off any excess, then enjoy!