Baking doughnuts eliminates the oily mess you might get from frying them and it reduces the amount of fat in the doughnuts. Unless you bake doughnuts regularly, there's no need for a specialty doughnut pan. Use balls of tinfoil or marbles to shape the holes as you bake the doughnuts, or cut the holes out after you've baked the doughnuts.
Placing balled up tinfoil in the center of each muffin cup is one way to bake doughnuts in a muffin pan. Roll a ball of tinfoil for each cup so it is 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 it down firmly to flatten the bottom of the ball so it doesn't roll around. Grease the muffin pan and tinfoil balls with cooking spray before piping in the batter and baking the doughnuts.
If you are baking doughnuts in a miniature muffin pan, you can convert it into a doughnut pan using standard-sized glass marbles. For a standard-sized muffin pan, you will need large glass marbles instead of their smaller counterparts. Either way, place the muffin pan on a flat surface and carefully set a marble in the center of each muffin cup before spraying it with cooking oil. Reset any marbles that are moved away from the center by the cooking spray and then pipe in the batter. Move the pan carefully to the oven so the marbles do not roll off center.
Once your baked doughnuts have cooled in the muffin pan, you need to remove the inserts. Poke the insert out of each doughnut and set them aside for later use or discard them. With the inserts removed, all that's left is to trim any excess batter that is obstructing the center hole of the doughnut. Use a small, sharp knife to cut away any ragged bits and then the doughnuts are ready to be iced or served immediately.
If you don't have foil or marbles on hand, you can still make doughnuts in a muffin pan. Start by filling each muffin cup halfway with batter and baking 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 cut-outs, known as doughnut holes, in a bowl. The doughnuts will not look perfect, but once they are coated in icing, it will be hard to tell they weren't made in a doughnut pan. The doughnut holes can be iced, coated in a sugar blend or served plain.