Pour vegetable oil into a heavy-bottomed pot until it reaches approximately 3/4 inch in depth.
Heat the oil to 375°F.
While the oil heats, place the eggs in a large mixing bowl.
Beat the eggs until foamy.
Add the milk and pure vanilla extract to the beaten eggs.
Whisk until the mixture is fully combined.
Add the all-purpose flour, baking powder, ground cinnamon, ground nutmeg, salt, and granulated sugar.
Mix until the batter is smooth and no dry flour remains.
Carefully drop spoonfuls of batter into the hot oil. A cookie scoop may be used to portion the batter evenly.
Fry the bites in small batches to avoid overcrowding the pot.
Cook until the bottoms are golden brown.
Carefully flip each bite and continue frying until the opposite side is golden brown and the centers are cooked through.
Remove the fried bites from the oil using a slotted spoon or tongs.
Transfer the bites to a paper towel-lined plate or tray to drain excess oil.
Repeat the frying process with the remaining batter.
Sprinkle the warm funnel cake bites generously with powdered sugar.
Serve immediately with optional dipping sauces, if desired.