Prep the Dough: In a mixing bowl, whisk the flour, sugar, baking powder, salt, and nutmeg together until well combined.
Combine Wet Ingredients: In another bowl, combine the milk, eggs, and melted butter. Whisk until fully combined.
Mix Together: Pour the wet ingredients into the dry ingredients, and stir until just combined. Do not overmix. The dough should be soft.
Heat the Oil: In a deep frying pan, heat about 2 inches of vegetable oil over medium heat (about 350°F).
Form the Donut Holes: Use a small cookie scoop or your hands to shape the dough into balls about 1 inch in size.
Fry the Dough: Carefully drop the balls into the hot oil, a few at a time, and fry until golden brown, about 2-3 minutes on each side. Use a slotted spoon to remove them and transfer to a paper towel-lined plate.
Prepare Chocolate Glaze: In a microwave-safe bowl, melt the chocolate chips and butter together in 30-second increments, stirring in between until smooth. Stir in powdered sugar until combined.
Glaze the Donut Holes: Dip each warm donut hole into the chocolate glaze, allowing any excess to drip off before placing them on a wire rack to set.