Preheat the oven to 375°F

Combine flour, sugar, baking powder, salt, and ground nutmeg in the bowl of a food processor or a bowl.

Turn on the food processor for a few seconds to combine these dry ingredients well, or whisk together if not using a food processor.

Cut cold butter into half-inch chunks by cutting it in half lengthwise, then cutting the 2 lengths in half lengthwise again. Then, cut half-inch chunks from the 4 lengths of butter.

Add cold butter to your flour mixture. If using a food processor, pulse several times until the mixture looks like cornmeal. You'll want to achieve the same cornmeal texture if you cut by hand.

If using a food processor, transfer the flour/butter mixture to a mixing bowl.

Whisk eggs and milk together.

Add grated apple and egg/milk mixture to the flour/butter mixture and fold in ingredients until just combined.

Spray your donut pan or mini-muffin pans with baking release spray.

Fill pans to just three-quarters full; err on the side of little rather than too much. I used my 1 ½ tablespoon cookie scoop but didn't fill it all the way.

Place in preheated oven for 6 minutes on a rack in the middle of the oven. Then, without opening the oven, lower the heat to 350°F and bake for another 6-7 minutes until the tops of the donut holes are golden brown.

While the donuts are baking, melt the 1/2 cup of butter in one bowl and combine the granulated sugar and nutmeg in a rimmed baking sheet.

Pour the butter into another rimmed baking tray.

When you remove that pan from the oven, increase the heat back to 375°, so it is ready for the next batch.

Let the doughnuts cool for 5 minutes, then coat them in the melted butter in the baking pan by gently moving the tray back and forth.

Then, transfer them to the baking tray with the sugar and gently coat them there by moving the tray back and forth.

Repeat with the remaining batter.