In a large bowl, mix flour, sugar, baking powder, salt, and nutmeg.
In another bowl, whisk eggs, milk, melted butter, and vanilla.
Combine wet and dry ingredients until just mixed.
Preheat your deep fryer or oil in a pot to 375°F (190°C).
Using a doughnut cutter, cut out shapes from the dough.
Carefully place doughnuts in hot oil, frying 2-3 at a time.
Fry each side for about 2-3 minutes until golden brown.
Remove doughnuts and place them on paper towels to drain excess oil.
For the glaze, mix powdered sugar with a little water until smooth.
Dip the tops of the cooled doughnuts in glaze and sprinkle with toppings.