Preheat a large nonstick skillet over medium high heat with 2 tablespoons of EVOO and brown the meatballs on all sides (work in batches if you need to). Once the meatballs are seared on the outside, remove them from the pan and reserve on a plate.
Add the remaining 1 tablespoon EVOO to the pan along with the onion, remaining 3 cloves of garlic, carrot, and bay leaf. Cook until the veggies begin to get tender, 4-5 minutes.
Add the tomato paste to the veggies and cook until the tomato paste caramelizes and smells sweet, 2-3 minutes. Add the tomatoes to the pot and mash them up with the back of a spoon or a potato masher. Add in the red wine and bring the sauce up to a bubble, scraping all of the brown bits off the bottom of the pan. Add the seared meatballs back to the pan and simmer for about 1-1 1/2 hours over medium-low heat, until sauce is flavorful and the meatballs are nice and tender.
When the meatballs have about 20 minutes left to cook, place a large pot of salted water over high heat and bring it to a boil. Add some salt and the spaghetti and cook to al dente, according to package directions. Drain the pasta and toss it in the pan with the sauce and the meatballs. To serve, top each portion of pasta with a few meatballs.