To make the meatballs, combine the parmesan, ricotta, eggs, salt, pepper, and oregano in a mixing bowl. Fold the meat in until just combined. Chill overnight.
Preheat the oven to 500°F.
To make the sauce, heat the olive oil in a small saucepan. Add the garlic and cook until golden. Add the carrots, celery and onions and cook until softened, about 7 minutes. Add the canned tomatoes, sugar and salt and bring to a simmer for 30 minutes. Remove from heat and stir in the basil. If you like smoother consistency, you can pulse the sauce with an immersion blender.
Form the meat mixture into 2-inch meatballs and arrange in a baking dish with sides. Roast for 8 minutes, turn the meatballs, and continue to cook until they register an internal temperature of 165°F. Add the sauce to the baking dish and continue cooking for 25 minutes.
Meanwhile, bring a large pot of salted water to a boil. Add the spaghetti and cook according to package instructions. Drain the pasta, return to the pot, and drizzle with olive oil.
To serve, place the cooked pasta in a serving dish. Top with meatballs, sauce, parmesan, and parsley for garnish.