In a large bowl, add in the flour, sugar, baking powder, cinnamon, nutmeg, and salt. Mix together with a whisk until combined.
Add in the egg, milk, melted butter, and vanilla extract. Mix together until it's combined.
Transfer the batter into a piping bag and pipe the batter into a greased donut pan. Fill each cavity about 80% full.
Bake at 350F/177C for 12 minutes
Make the cinnamon sugar topping by mixing together the sugar and cinnamon in a bowl.
Toss donuts into the cinnamon sugar mixture while donuts are still warm. Warm donuts will stick to the cinnamon sugar better. If it's not sticking then dip the donuts into some melted butter before tossing it into the cinnamon sugar.
Notes
The donut pan I used has cavities that are 2.75inches/7cm in diameter.