Preheat oven to 350F degrees.
Heat a large skillet over medium heat. Crumble the ground beef in to the skillet and cook, stirring often, until completely browned. Remove the beef from the pan and set aside. Drain the fat from the pan.
Add the butter to the skillet and melt over medium heat. When the butter is melted, add the diced onion and bell pepper and saute until softened, about 5 minutes.
Add the browned beef back to the skillet. Add the Worcestershire sauce, ketchup, salt, and pepper; mix well. Cook the mixture for about 2 minutes over medium heat, stirring occasionally.
Fill the cooked pasta shells with the meat mixture and place in an even layer in a glass baking dish.
Add half of the cheddar cheese cubes to the stuffed shells (we stuffed two cheese cubes into each shell).
In a medium sauce pan, whisk together the milk, beef broth, and cornstarch. Heat the mixture over medium heat until hot, then add the remaining cheddar cheese; stir until melted and the sauce thickens. Pour half of the sauce over the stuffed shells in the pan.
Bake the stuffed shells at 350F for 10 minutes, or until the cheese is melted.
Serve hot with the extra cheese sauce on the side.