In a large bowl, mix flour, sugar, baking powder, salt, and nutmeg.
In another bowl, whisk milk, eggs, melted butter, and vanilla together.
Add wet ingredients to the dry ingredients and mix until combined.
Heat oil in a deep fryer or large pot to 350°F (175°C).
Using a donut cutter, cut out shapes from the dough.
Carefully place the donuts in the hot oil, frying a few at a time.
Fry for about 2-3 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 icing.
Decorate with icing and sprinkles as desired.