Heat a large skillet over medium-high heat. Cook and stir the ground beef with a sprinkle of salt and pepper until it’s browned and crumbly, about 5-7 minutes. Drain off the grease.
Add the onion, bell pepper, carrot, and garlic to the beef. Cook and stir until the onion is lightly browned and fragrant, roughly 15 minutes.
Stir in the diced tomatoes, tomato sauce, mushrooms, Worcestershire sauce, and brown sugar. Season with an extra pinch of salt and pepper if needed. Reduce heat to low and let the mixture simmer for 45 minutes, stirring occasionally, until the liquid reduces and the flavors meld.
Preheat your oven to 350°F (175°C).
While the sauce simmers, bring a large pot of salted water to a boil. Cook the bow-tie pasta until al dente, about 12 minutes. Drain the pasta and transfer it to a 9x13-inch casserole dish.
Spread the cream of mushroom soup evenly over the pasta. Spoon the beef and vegetable mixture over the top, spreading it out evenly. Sprinkle the shredded cheddar cheese across the surface.
Bake the casserole in the preheated oven for 45 minutes, or until it’s bubbling and the cheese is melted and golden brown.