1) Preheat the oven to 425°F. Lightly grease two standard doughnut pans.
2) In a medium-sized mixing bowl, beat together the butter, vegetable oil, and sugars until smooth.
3) Add the eggs, beating to combine.
4) Stir in the baking powder, baking soda, nutmeg, salt, and vanilla.
5) Stir the flour into the butter mixture alternately with the milk, beginning and ending with the flour and making sure everything is thoroughly combined.
6) For chocolate chip doughnuts, stir in the chocolate chips.
7) For coconut doughnuts, sprinkle 1 teaspoon toasted shredded coconut into each of the wells of the pans.
8) Spoon the batter into the lightly greased doughnut pans, filling the wells to about 1/4" shy of the rim for coconut or cinnamon doughnuts; or to the rim for chocolate chip doughnuts.
9) Bake the doughnuts for 10 minutes. Remove them from the oven, and wait 5 to 7 minutes before turning them out of the pans onto a rack. Enjoy warm; or cool completely, and store airtight.
10) For cinnamon doughnuts, shake warm doughnuts in a plastic bag with about 1/4 to 1/3 cup cinnamon-sugar. For sugar-coated chocolate chip doughnuts, shake doughnuts in a plastic bag with about 1/2 cup non-melting white sugar (for best results), or confectioners' sugar.
Yield: 12 doughnuts.