Preheat the oven to 350 degrees F.
Spray donut pans with the baking spray and set aside.
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, filling each one about three-quaters full.
Bake for 20 minutes or until the donuts are lightly browned.
Cool for 5 minutes on donut pan before removing them.