For Baked Donuts:
Preheat the oven to 350°F (175°C) and grease a donut pan.
Mix dry ingredients: In a large bowl, whisk together flour, sugar, baking powder, salt, and nutmeg.
Combine wet ingredients: In a separate bowl, whisk together milk, eggs, melted butter, and vanilla extract.
Mix the batter: Gradually add the wet ingredients to the dry ingredients, stirring until just combined.
Fill the donut pan: Spoon or pipe the batter into the donut molds, filling each about ¾ full.
Bake for 12-15 minutes or until lightly golden and a toothpick inserted comes out clean.
Cool slightly, then transfer to a wire rack.
Coat in powdered sugar: While still slightly warm, toss the donuts in a bowl of powdered sugar until evenly coated.
For Fried Donuts:
Heat oil in a deep pan to 350°F (175°C).
Prepare the dough following the steps above, but instead of baking, shape the dough into small rounds.
Fry in batches, cooking each side for 1-2 minutes or until golden brown.
Drain on a paper towel to remove excess oil.
Coat with powdered sugar while still warm.