Preheat the oven to 425°F. Lightly grease doughnut pans and 12-cup mini muffin tin.
In a medium-sized mixing bowl, cream together the butter, vegetable oil, and sugars till smooth. Add the eggs, beating to combine. Add the vanilla and stir to combine.
In a separate bowl. stir the baking powder, baking soda, nutmeg, cinnamon, salt, and flour until well combined. Add 1/3 of the mixture at a time to the butter mixture alternately with the milk, beginning and ending with the flour and making sure everything is thoroughly combined.
Spoon the batter into a pastry bag without a tip. Squeeze into the doughnut molds, filling the cups nearly full. Bake the doughnuts for 5 minutes and then drop temperature to 375. Continue to bake for 10 more minutes, or until they’re a pale golden brown and a cake tester inserted into the middle of one of the center muffins comes out clean. (Only bake 7 more minutes if they are in a mini muffin tin)
In a medium bowl, add the powdered sugar. Melt the butter in a separate small bowl. When muffins have cooled slightly, roll the doughnuts/doughnut holes in the butter and then the powdered sugar. Cover in powdered sugar until completely coated. This may take a couple coats of powdered sugar.
Serve immediately or within 24 hours.