Heat the oven to 375°F and grease a 9-by-13-inch baking dish. Cook noodles in a large pot of water with the tablespoon salt until 2 minutes short of the package time, then drain.
Meanwhile, brown beef, onion and bell pepper in a large skillet for 8 minutes until the meat reaches 160°F, breaking it into crumbles. Drain excess fat.
Add tomato sauce, ketchup, brown sugar, vinegar, Worcestershire, sauce salt and pepper. Simmer for 8 to 10 minutes until lightly thickened.
Fold in the drained noodles and transfer to the baking dish. Scatter cheddar evenly over the surface.
Bake for 18 to 22 minutes until bubbling and golden in places. Rest for 5 minutes before serving.