Preheat broiler on high. Make sure oven rack is about 4 inches below the heat source. Rub 1 teaspoon olive oil over the surface of a rimmed baking sheet.

In a large sauce pot, heat the remaining 5 teaspoons olive oil over medium heat. Add two cloves of garlic and cook until golden, about 3 minutes. Add tomatoes, 1/2 teaspoons salt, sugar, and 1/2 teaspoon red pepper flakes (if desired). Bring to a boil, reduce heat, and simmer, covered, for 10 minutes.

Meanwhile, in a food processor, combine zucchini, carrot, onion, remaining garlic, and parsley. Pulse until finely chopped. Transfer vegetable mixture to a large bowl. Add the beef, oats, parmesan, remaining salt, remaining red pepper flakes (if desired), and egg. Mix well.

Shape mixture into meatballs 1 1/2 inches in diameter. Arrange evenly on the prepared baking sheet. Broil until the tops of the meatballs are browned, about 5 minutes.

Gently transfer meatballs to the sauce pot and continue to cook, covered, for 10 minutes or until meatballs are cooked through. Remove from heat.

Serve as an appetizer or over cooked spaghetti as a main course. Garnish with additional parsley and parmesan if desired.