In a large mixing bowl, whisk together the flour, 1/2 cup sugar, baking powder, salt, ground cinnamon, and nutmeg until well combined.
In another bowl, mix the milk, egg, and melted butter until smooth.
Pour the wet ingredients into the dry ingredients, stirring gently until just combined. Be careful not to overmix; a few lumps are okay.
Heat oil in a deep fryer or heavy pan to 350°F (175°C). Ensure there's enough oil to submerge the donut holes.
Using a small cookie scoop or your hands, portion out about 1 tablespoon of the batter and carefully drop them into the hot oil (working in batches to avoid overcrowding).
Fry the donut holes for about 2-3 minutes on each side, or until they are golden brown.
Remove the donut holes using a slotted spoon and transfer them to a paper towel-lined plate to drain excess oil.
In a separate bowl, combine the 1/2 cup sugar and 1 tablespoon cinnamon for the coating.
While they are still warm, roll each donut hole in the cinnamon sugar mixture until fully coated.