Baking doughnuts instead of frying eliminates the oily mess and reduces the amount of fat. Unless you bake doughnuts regularly, there's no need for a specialty pan—a muffin pan will do. Just use balls of tinfoil or marbles to shape the holes, or cut the holes out after baking. (Doughnut holes, anyone?)
Tinfoil Inserts
Roll a ball of tinfoil for each muffin cup, approximately the size you would like the doughnut holes to be. Pack the tinfoil ball tightly to minimize areas for the batter to seep into. Place a tinfoil ball into a muffin cup and press the ball down firmly to flatten the bottom so it doesn't roll around. Grease the muffin pan and tinfoil balls with cooking spray. Pipe in the batter and bake the doughnuts.
Glass Marble Inserts
If you're baking doughnuts in a miniature muffin pan, you can use standard-sized glass marbles. For a regular muffin pan, you'll need large glass marbles.
Place the muffin pan on a flat surface and carefully set a marble in the center of each cup. Spray the cup and marble it with cooking oil. Reset any marbles that roll away from the center. Pipe in the batter. Move the pan carefully to the oven so the marbles don't roll off center.
Removing the Inserts
Once the baked doughnuts have cooled in the muffin pan, poke the insert out of each doughnut and set the inserts aside for later use or discard them. Trim any excess batter obstructing the center hole with a small, sharp knife. Ice the doughnuts or serve immediately.
Make Doughnuts and Doughnut Holes
If you don't have foil or marbles, you can still make doughnuts in a muffin pan. Fill each muffin cup halfway with batter and bake them as you normally would. Once the doughnuts have cooled, remove them from the muffin cups. Use a small, sharp knife to cut a circle out of each doughnut, and place the doughnut holes in a bowl. The doughnuts won't look perfect, but once they're coated in icing, they'll look delicious. The doughnut holes can be iced, coated in a sugar blend, or served plain.