In a mixing bowl, combine flour, sugar, baking powder, salt, and nutmeg.
In another bowl, whisk together milk, eggs, melted butter, and vanilla extract.
Add the wet ingredients to the dry ingredients and mix until just combined.
Preheat oil in a deep fryer or heavy pot to 375°F (190°C).
Using a donut cutter, cut out donuts from the dough.
Carefully drop donuts into the hot oil, frying a few at a time.
Fry each donut for about 1-2 minutes on each side until golden brown.
Remove donuts and place them on a paper towel to drain excess oil.
Let them cool slightly before glazing or topping.
Enjoy your delicious homemade donuts!