Preheat oven to 350°F (175°C). Grease a 9x13-inch baking dish.
Brown ground beef in a skillet over medium heat, then drain fat. Add onion, bell pepper, and garlic. Cook for 5 minutes until soft and fragrant.
Stir in tomato sauce, ketchup, brown sugar, Worcestershire sauce, mustard, salt, and pepper. Simmer on low for 5–10 minutes.
Mix cooked pasta with the sloppy joe mixture and 1 cup of cheddar in a large bowl.
Spread the mixture evenly into the greased baking dish.
Top with remaining cheese. Add crushed crackers or French fried onions if using.
Bake uncovered for 20–25 minutes, until the cheese is bubbly and lightly golden.
Let sit for 5 minutes before serving for easier slicing and better texture.