Preheat an oven to 350 degrees F (175 degrees C). Lightly grease a baking sheet.
Beat the egg in a mixing bowl, then stir in the carrot, zucchini, onion, salt, basil, and oregano. Add the turkey and Parmesan cheese; mix until evenly blended. Form the turkey mixture into 16 meatballs, roll in bread crumbs, and place onto the prepared baking sheet.
Bake in the preheated oven until the turkey is no longer pink on the inside, and the meatballs are golden brown, about 1 hour.
