In a large bowl, mix together the flour, sugar, baking powder, cinnamon, nutmeg, and salt. In a small bowl, whisk together the egg, milk, melted butter, and vanilla.
Add the wet mixture into the dry ingredients and mix with a spatula until just combined and dissolving all lumps. Add the batter into the donut baking molds.
Brush each donut (not all at once) with the melted butter or dip each donut first in the butter and then in the cinnamon sugar, on one or both sides. Your choice 😉