In a large bowl, whisk together the flour, sugar, salt, baking powder, and nutmeg.
In a separate bowl, combine the milk, eggs, and melted butter, then mix well.
Gradually add the wet ingredients to the dry ingredients, stirring until combined.
On a lightly floured surface, roll out the dough to about 1/2 inch thick.
Use a doughnut cutter to cut out doughnuts and holes.
Heat oil in a deep fryer or heavy pot to 375°F (190°C).
Carefully place doughnuts in the hot oil, a few at a time.
Fry until golden brown, about 1-2 minutes per side.
Remove and drain on paper towels.
While warm, dip in glaze or sprinkle with powdered sugar.