Preheat the oven to 400°F. Line a baking sheet with parchment paper or lightly grease it with cooking spray.
In a large mixing bowl, combine the grated carrots, shredded potatoes, breadcrumbs, Parmesan cheese, egg, garlic powder, onion powder, salt, black pepper, and paprika. Mix until well combined.
Using your hands, form the mixture into small tot shapes, about 1 to 1.5 inches long. Place the formed tots on the prepared baking sheet, leaving space between each one.
Lightly spray the tops of the tots with cooking spray or drizzle with a little oil for added crispiness.
Bake in the preheated oven for 20-25 minutes, or until golden brown and crispy, flipping halfway through for even cooking.
Remove from the oven and let cool for a few minutes before serving.