Cook the pasta to al dente according to the package directions; drain and set aside.
Heat the oil in a 5-quart pot over medium to medium-high heat. Add the beef, onion, and celery, and cook (uncovered) until the beef is browned and the vegetables are softened but not browned, about 8 to 10 minutes, stirring occasionally. Turn the heat down to medium and add the carrot, tomato, and garlic and cook 2 minutes more, stirring frequently.
Stir in the flour and cook 30 seconds, then stir in the milk, water, ketchup, mustard, Worcestershire, salt, and pepper. Cook (uncovered) over medium heat until it reaches a gentle boil. Turn off the heat and stir in the cheese, and then the pasta.
Serve topped with any garnishes you like.
Notes
Nutrition information was calculated without garnishes.