Step 1

Preheat the oven to 350 degrees. Spray 2 doughnut pans well.

Step 2

Into a large bowl, sift together the flour, sugar, baking powder, cinnamon, nutmeg, and salt. In a small bowl, whisk together the egg, milk, melted butter, and vanilla. Stir the wet mixture into the dry ingredients until just combined.

Step 3

Spoon the batter into the baking pans, filling each one a little more than three-quarters full. Bake for 17 minutes, until a toothpick comes out clean. Allow to cool for 5 minutes, then tap the doughnuts out onto a sheet pan.

Step 4

For the topping, melt the 8 tablespoons of butter in an 8-inch saute pan. Combine the sugar and cinnamon in a small bowl. Dip each doughnut first in the butter and then in the cinnamon sugar, either on one side or both sides.