Sauté onions and garlic together with olive oil until soft and translucent, add pepper and mushrooms - continue to cook until peppers are tender. Add tomatoes (chopped) and their liquid, tomato sauce, and seasonings. Continue to cook (covered) for about 25 minutes on low heat to transfer flavors.
Combine ground beef and pork in a glass bowl, add three crushed garlic cloves, and two finely diced onions. Mix in one cup fine breadcrumbs, seasonings, Parmesan cheese and two eggs. Combine well. Form into 1½" (4 cm) balls and place on parchment paper.
Bake in a 350°F 180°C oven, turning frequently until done (about 20 minutes) - do not overcook!
Add the meatballs carefully to the tomato sauce mixture in stages and gently mix after a few minutes cooking when they have started to solidify.
Simmer for 45 - 60 minutes, skimming off any excess fats from the surface of the sauce.
Serve with spaghetti, and Parmesan cheese.