Heat the oil in your deep fryer to 190° C (375° F).
Add the flour, sugar, salt, baking powder, cinnamon, and nutmeg to a mixing bowl. Whisk together. Add the egg to a measuring cup and add the milk, whisk together with a fork. Melt the butter.
Stir in the butter and mix until crumbly.
Stir in the beaten egg and milk until mixture is smooth, if dough seems too thin, sprinkle in a tablespoon of flour. The dough is very sticky but do not let that concern you.
Place dough on a well floured work surface and roll out with a well floured pin to about ¼ inch thickness.
Using a donut cutter or different sized biscuit cutters, cut dough into rings.
Carefully place 2-3 rings, plus the holes, in the deep fryer depending on the size of the fryer, use of the basket is your preference. Fry for about 2-3 minutes, turning when the bottom is golden brown. The holes basically turn themselves over. I cooked two donuts at a time, plus their holes. The basket is in the fryer but I placed the donuts in with my hands and used chop sticks to turn them and remove them.
Drain the cooked donuts on paper towels, let the oil reach the cooking temp again, and continue until all batches are fried. Serve and enjoy.