Preheat the oven to 425°F. Lightly grease 2 donut pans.
In a medium-sized mixing bowl or mixer beat together the butter, vegetable oil, granulated, and brown sugar until smooth. Add the eggs and beat until well combined.
Mix in baking powder, baking soda, nutmeg, salt, and vanilla, until batter comes together.
Mix in the flour and milk, adding the flour and alternating with the milk, beginning and ending with the flour. Mix batter until smooth and well combined.
Gently spoon the batter evenly into the lightly greased doughnut pans, filling until just shy of the rim.
Place pans in the oven and bake for 9-10 minutes. Remove from oven, allow donuts to cool for 5 minutes before you remove from the pans. Prepare frosting during this time.