Roughly chop carrot, zucchini and onion, then transfer to a food processor. Process until finely chopped. Alternatively, use a box grater to grate the vegetables.
Place processed vegetables on a tea towel and wring out as much liquid as possible. Transfer strained vegetables to a large mixing bowl. Save the liquid for the marinara sauce.
Add the rest of the ingredients for the meatballs (except for marinara sauce) to the mixing bowl. Mix until combined.
Preheat oven to 350˚F / 180˚C and line a baking sheet with parchment paper.
Take a large spoonful of mixture and shape it into a ball with your hands, then transfer to lined baking sheet. Repeat until all the mixture is used up. Try to keep all the meatballs the same size so they cook evenly.
Bake meatballs for 15 minutes, flip, then bake fo 15 more minutes.
In a large nonstick skillet, heat up marinara sauce. Mix in the veggie liquid from before.
Remove meatballs from the oven and carefully transfer them to the skillet. Stir to coat the meatballs in sauce evenly. Remove from heat and serve immediately with pasta or sides of choice.