Preheat the oven to 375°F. Spray a donut pan with nonstick baking spray.
Beat the butter and sugars until creamy. Add the egg, extracts, and sour cream and beat again. The mixture will look grainy.
Stir together the baking powder, baking soda, flour, and nutmeg. Slowly add the flour mixture and eggnog to the butter mixture until stiff dough forms.
Spoon the dough into a large Ziploc bag and cut one corner off. Make sure it is large enough to press the dough through without splitting the bag.
Fill the donut pan cavities at least half full. Bake for 10-11 minutes. Do not over bake. Remove and let the donuts cool in the pan for 2 minutes. Gently remove the donuts and place on a wire rack to cool completely.
Wipe the pan out with a paper towel, spray it again, and repeat with the remaining dough.
Whisk together the powdered sugar and eggnog until creamy. Spread on the tops of the cooled donuts using a metal spatula. The glaze sets up quickly so sprinkle the tops of the donuts with nutmeg as soon as you add the glaze to each one. Let the glaze set completely before storing in a tightly sealed container.