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Begin by preheating your oven to 375 degrees Fahrenheit. Lightly coat a baking sheet with olive oil and set it aside for later use.
Chop the sweet potato and carrot into 3 to 4 sizable pieces. Transfer them into a food processor equipped with a metal blade and pulse until they are finely chopped to resemble rice-sized bits.
In a large skillet, heat over medium heat and add a light spray of oil. Introduce the chopped vegetables into the skillet and sauté, stirring occasionally for about 5 minutes, or until they become tender. Once softened, move the mixture to a large bowl. Add the egg, panko breadcrumbs, mozzarella cheese, onion powder, garlic powder, smoked paprika, salt, and pepper. Use a spatula to mix everything thoroughly until well combined.
Using your hands, carefully shape the sweet potato and carrot mixture into small rectangular shapes, about 1 tablespoon each, pressing and rolling them together firmly. Arrange these formed pieces evenly on the prepared baking sheet, give them a light spray of olive oil, and bake in the oven for 10 minutes. Afterward, take them out, gently flip each tot using your hands or a small spatula, return them to the oven, and continue baking for an additional 10 to 12 minutes, or until they achieve a golden brown and crispy exterior. This recipe yields 30 tots.