Place the grated potatoes in a bowl of cold water and let them soak for 5 minutes to remove excess starch.
Drain the potatoes well, then wrap them in a clean kitchen towel and squeeze out as much moisture as possible.
In a mixing bowl, combine the potatoes with the egg, Parmesan, flour, salt, garlic powder, paprika, and black pepper.
Shape the mixture into small tot-shaped cylinders or nuggets.
For frying: heat the oil in a skillet to 350°F (175°C) and fry the tots in batches for 3 to 4 minutes, until golden and crisp. For baking: place the tots on a greased baking sheet, spray lightly with oil, and bake at 425°F (220°C) for 20 to 25 minutes, turning halfway through.
Drain fried tots on paper towels or let baked tots cool for a minute, then serve hot with dipping sauce of choice.