Grease the donut pans really well (I use butter). Set them aside.
In a large mixing bowl, sift the flour, baking powder, and cinnamon together. Then add the nutmeg, sugar and salt and whisk together to combine.
In another small bowl, whisk together the milk, melted butter, vanilla, and egg until they're all combined.
Pour the wet ingredients into the dry ingredients and whisk together until just combined. Don't overmix it. It's OK if you see a few small lumps in the batter.
Spoon the batter into the donut cavities, about ¾ full.
Bake the donuts for 17-20 minutes, or until a toothpick inserted in one comes out clean.
Let the donuts cool in the pans for about 10 minutes before removing them . Then transfer them to a wire rack to cool completely.
Make the topping
Stir together the sugar and the ground cinnamon in a small bowl.
Quickly dunk the donuts in the melted butter on both sides. For less sweet donuts, you can dunk them on one side only. Alternatively, use a pastry brush to brush the melted butter on them. Don't soak the donuts in the butter too long because they'll get soggy.
Dip the donuts in the cinnamon mixture.
Enjoy!
Notes
These cinnamon sugar donuts taste best when served immediately. However, you can store them in an air-tight container at room temperature for up to about 2-3 days.