Use a handmixer to beat together the butter, veggie oil, brown sugar, and granulated sugar in a large bowl until smooth.
Beat in the eggs, one at a time to make sure each one is fully incorporated into the batter.
Switch to a wooden spoon or spatula (you're done with the handmixer now) and stir in the vanilla, nutmeg, baking soda, baking powder, and salt into the batter.
Add the flour and the milk to the batter, alternating between each addition and stiring until ingredients are just combined; you don't want to overmix, but you don't want to see streaks of flour or puddles of milk, either.
Fill each mini muffin tin cavity to just about 3/4 of the way -- which is about 2 tsp of batter per cavity. These donut holes will poof up a lot in the oven, and we're aiming for a ball shape instead of a muffin shape.
Bake the donut holes at 325F for 9-10 minutes, or until a toothpick inserted into the center comes out with just a few crumbs clinging to it. Do not overbake!
Remove donut holes from oven. Let cool 3-5 minutes in the tins, then turn them out onto a wire cooling rack. When they're completely cool, roll them in the powdered sugar and serve.**