Pre-heat your oven to 375 degrees.
In a large bowl, sift together the flour, sugar, baking powder, cinnamon, nutmeg and salt.
In a separate bowl, whisk the egg, milk, melted butter and vanilla extract. Set the wet and dry ingredients aside while you do some apple grating.
Peel your apple and grate it using the large holes on a box grater. (If you don’t have a box grater, relax. Just use a sharp knife to chop your apple very finely.) Use your hands to squeeze as much of the juice from the grated apple as you can, and add the squeezed grated apple to the dry ingredients.
Fold the wet ingredients into the dry ingredients until just combined. DO NO OVER-MIX, people. (Over-mixing creates overly dense doughnuts.)
Spray the mini muffin tin and evenly distribute the doughnut batter amongst the wells. (You should have enough for about 14 doughnut holes.)
Bake your doughnut holes for 10-12 minutes until they are lightly browned. Allow the doughnut holes to cool for 1-2 minutes before removing them from the tin and place them on a rack to cool for at least 10 minutes.
While your doughnut holes are cooling, prepare the topping. In a small pan melt the butter and set aside to cool. In a separate bowl, combine the cinnamon and sugar.
When the doughnuts holes are cool, coat each one with butter (you can dip them in the butter or use a pastry brush) and then roll it in the cinnamon-sugar mixture. Don’t skimp on the cinnamon-sugar, friends. You want a really solid coating. Serve immediately.