Preheat the oven to 375°F and lightly grease two standard doughnut pans to ensure easy removal of the baked doughnuts.
In a medium-sized mixing bowl, beat together the butter, vegetable oil, and sugars until smooth to create the base of the doughnut batter.
Add the eggs to the butter mixture, beating to combine and incorporate them thoroughly into the batter.
Stir in the baking powder, baking soda, nutmeg, salt, and vanilla to add flavor and leavening to the doughnut batter.
Gradually stir the flour into the butter mixture alternately with the milk, ensuring thorough mixing and a consistent batter texture.
The batter will be fairly thick; when you draw your spatula through the batter, it will leave a furrow, indicating proper consistency.
Spoon the batter into the lightly greased doughnut pans, filling the wells to about 1/4" shy of the rim to allow room for rising during baking.
Bake the doughnuts for 10 to 12 minutes until they are golden brown and fully cooked through, providing a delightful aroma in your kitchen.
Remove the baked doughnuts from the oven, and let them rest for 5 to 7 minutes before gently turning them out of the pans onto a cooling rack.
For cinnamon doughnuts, shake warm doughnuts in a plastic bag with about 1/4 to 1/3 cup cinnamon sugar, coating them evenly for a sweet and spicy finish.
Alternatively, for sugar-coated doughnuts, shake them in a plastic bag with about 1/2 cup non-melting topping sugar or confectioners' sugar for a classic sweet coating.
For frosted doughnuts, explore our three easy doughnut glaze recipes to add a luscious and flavorful finish to your baked treats.