Add all of the ingredients to a large bowl except for the carrot and zucchini.
Peel and grate the carrot and add to the bowl. Peel, grate, and squeeze the water out of the zucchini in a separate bowl. (I used paper towels but a kitchen towel works, too). Then add to the bowl.
Combine all ingredients. It will be wet and sticky. Wetting your fingers with water will help. Roll into meatballs and put in the oven for 35 minutes.