Place the grated potatoes in a clean kitchen towel and squeeze out as much moisture as possible. This will help the pancakes crisp up nicely.
In a large mixing bowl, combine the drained grated potatoes, mozzarella cheese, flour, egg, garlic powder, onion powder, salt, black pepper, and green onions (if using). Mix until well combined.
Heat a large skillet over medium heat and add enough vegetable oil to coat the bottom of the pan.
Once the oil is hot, scoop about 1/4 cup of the potato mixture and flatten it into a pancake shape in the skillet. Repeat with additional pancakes, making sure not to overcrowd the pan.
Cook each pancake for about 4-5 minutes on one side, or until golden brown, then flip and cook for another 4-5 minutes on the other side.
Transfer the cooked pancakes to a paper towel-lined plate to drain excess oil. Repeat with the remaining mixture.
Serve hot with your favorite dipping sauce, such as soy sauce or a spicy mayo.