Preheat the oven to 425°F. Lightly grease two standard doughnut pans.
In a medium-sized mixing bowl, beat together the butter, vegetable oil, and sugars until smooth.
Add the eggs, beating to combine.
Stir in the baking powder, baking soda, salt, and vanilla.
Stir the flour into the butter mixture alternately with the milk, beginning and ending with the flour and making sure everything is thoroughly combined.
Spoon the batter into the lightly greased doughnut pans, filling the wells to about 1/4" shy of the rim.
Bake standard doughnuts for 9-10 minutes or mini's for 4-5. Remove them from the oven, and wait a few minutes before turning them out of the pans onto a rack.
Mix up glaze and dip tops of doughnuts into glaze and sprinkle with desired toppings.