Preheat oven to 375 degrees and lightly spray a sheet pan with olive oil. Set aside.
Cut sweet potato and carrot into 3 or 4 large chunks. Place them in a food processor fitted with a metal blade and process until finely chopped into rice-size pieces.
Heat a large skillet over medium heat, spray the pan with oil and add the chopped vegetables. Cook, stirring for 5 minutes, until softened. Transfer to a large bowl with the egg, panko, mozzarella, onion powder, garlic powder, smoked paprika, salt and pepper and stir with a spatula to ensure it is evenly combined.
With your hands, gently form sweet potato-carrot mixture into small rectangular pieces, pressing and rolling them firmly together about 1 tablespoon each. Evenly space them on prepared sheet pan, spray with olive oil and bake for 10 minutes. Remove from oven, using your hands or small spatula, flip each over, put them back in the oven and bake for 10-12 more minutes, or until brown and crisp. Makes 30 tots.