Heat olive oil in a large pot over medium heat. Add onion, parsley, basil, and garlic; cook and stir until onions are soft, about 5 minutes. Add pork and beef neck bones; cook and stir until browned, 7 to 10 minutes.

Stir crushed tomatoes slowly into the onion mixture; mix in salt, oregano, and bay leaves. Cook, covered, until flavors combine, about 2 1/2 hours. Stir in tomato paste; simmer uncovered until sauce thickens, about 2 hours.