Sauté the vegetables: Heat the butter (3 tablespoons) in a large pot over medium-high heat. Add the onions (1 large), green bell pepper (1), and garlic (1 tablespoon) and sauté until softened, about 8–10 minutes.
Brown the beef: Add the ground beef (2 pounds), salt (1 1/2 teaspoons), and pepper (1/2 teaspoon) and continue to cook, crumbling the beef with a spoon, until there is no longer any pink in the beef, about 5–6 minutes.
Build the sauce: Add tomato sauce (2 cans), crushed tomatoes with their juices (1 can), water (3 cups), Worcestershire sauce (1 tablespoon), paprika (1 teaspoon), sugar (2 teaspoons), and dried Italian seasoning (1 tablespoon) and bring to a simmer.
Simmer: Reduce the heat to low, cover, and simmer for 20 minutes, stirring occasionally.
Cook the pasta: Add the pasta (2 cups), partially cover, and simmer until the pasta is al dente, about 20–25 minutes.
Add the cheese: Sprinkle the top with mozzarella (16 ounces), cover, and cook on low for 2–3 minutes.
Rest and serve: Remove from the heat and let rest, covered, for 5–7 minutes. Sprinkle with parsley (2–3 tablespoons), if desired, and serve.