In a large mixing bowl, beat together 1 ½ cups of flour with the sugar, baking powder, salt, cinnamon, nutmeg, shortening, and milk. Use an electric mixer to ensure the batter is smooth and well combined.

Continue beating the mixture for 2 minutes until it's creamy and well-mixed.

Slowly stir in the remaining 2 cups of flour until the dough comes together. It should be soft but not too sticky.

On a well-floured surface, roll out the dough to about ½-inch thickness. Use a doughnut hole cutter or a small round cutter to cut out doughnut holes. Re-roll the scraps and continue cutting until all the dough is used up.

In a deep frying pan or pot, heat the oil to 350°F (175°C). Use a candy or frying thermometer to ensure the oil maintains its temperature. The oil should be deep enough for the doughnut holes to float while frying.

Carefully drop the cut doughnut holes into the hot oil, making sure not to overcrowd the pan. Fry them for approximately one minute on each side or until they are golden brown.

Once fried, remove the doughnut holes using a slotted spoon and place them on a plate lined with paper towels to drain excess oil. Allow them to cool slightly.

While they're still warm, either roll the doughnut holes in a mixture of cinnamon and sugar or dip them into the glaze. Let them sit for a few minutes to allow the glaze to set, if using.

Glaze (optional):

2 cups powdered sugar

4-5 tablespoons milk or water

1 teaspoon pure vanilla extract

Whisk all the ingredients together in a bowl until smooth. Adjust the amount of milk or water to achieve the desired consistency.