Preheat oven to 375°F. Grease a 9x13-inch baking dish.
Boil noodles in salted water until just shy of al dente; drain and set aside.
Warm oil in a large skillet over medium-high heat. Brown the beef, breaking it up, then drain excess fat.
Stir in onion and bell pepper. Cook until softened, about 4 minutes. Add garlic and cook 30 seconds.
Add tomato sauce, ketchup, tomato paste, broth, Worcestershire, mustard, brown sugar, paprika, chili powder, salt, pepper, and red pepper flakes. Simmer until glossy and thick, 5–7 minutes.
Toss noodles with the sauce and half of the cheese. Spread mixture in the prepared dish.
Sprinkle remaining cheese on top. Bake until bubbly and cheese is melted, 15–18 minutes. Broil 1 minute for extra color, if desired.
Rest 5 minutes before serving. Taste and adjust salt if needed.