In a large bowl, whisk together the flour, granulated sugar, baking powder, salt, and nutmeg (if using).
In a separate bowl, whisk together the eggs, milk, melted butter, and vanilla extract.
Add the wet ingredients to the dry ingredients and stir until just combined. The dough will be sticky.
Heat the Oil:
Pour vegetable oil into a deep fryer or large, heavy-bottomed pot to a depth of about 2 inches. Heat the oil to 350°F (175°C). Use a thermometer to maintain the temperature.
Fry the Dough Balls:
Using a small cookie scoop or two spoons, drop small balls of dough (about 1-2 tablespoons each) into the hot oil. Be careful not to overcrowd the pot; fry in batches if necessary.
Fry the dough balls for about 2-3 minutes per side, or until they are golden brown and cooked through. Use a slotted spoon to turn them as needed to ensure even cooking.
Remove the fried balls from the oil and place them on a plate lined with paper towels to drain excess oil.
Coat the Fried Balls:
While the fried balls are still warm, roll them in powdered sugar or granulated sugar to coat. Alternatively, you can drizzle them with a simple glaze made from powdered sugar and milk.
Serve and Enjoy:
Serve the fluffy fried balls warm. They are best enjoyed fresh but can be stored in an airtight container for a day or two.
Enjoy your delicious, fluffy fried balls!