In a medium bowl, mix the dry ingredients: flour, granulated sugar, baking powder, salt, and nutmeg.
In another medium bowl, mix milk, eggs, and vanilla well. Add melted butter and thoroughly combine.
Add the dry ingredients to the liquid mixture until all the ingredients are fully incorporated. Set aside.
Fill a medium pot with at least 3 inches (5cm) of oil. Note: Too little oil causes the donut holes to flatten.
Heat to 375℉ (175℃). A thermometer ensures the oil reaches the desired temperature.
While it heats, line a plate or baking sheet with paper towels to drain the fried donut holes.
Once the oil reaches 375℉ (175℃), turn the heat down to medium-low and start frying.
Scoop 1-2 tablespoons of dough with an ice cream scoop or spoon and gently drop it into the hot oil. Fry in batches to avoid overcrowding the pan. Too many at a time cools the oil too much, resulting in soggy sweets.
Fry for a few minutes, 1-2 minutes, or until one side is golden brown. Flip the doughballs over and fry for 1-2 more minutes or until the other side is golden brown and the holes are cooked through.
Use a large slotted spoon or skimmer to remove the donut holes from the oil. I usually place them on paper towels immediately to soak up the excess oil before transferring them to a serving plate. Do a taste test before proceeding with the next batch of donuts.
Continue with the rest of the batter until all has been fried.
If glazing, prepare the glaze while the donut holes are still warm. If using cinnamon sugar, roll them in the cinnamon sugar mixture while still hot so the sugar sticks. Enjoy.