In a medium kettle, brown beef until slightly pink. Add onion, celery, potatoes, and carrots. Cook till vegetables start to become tender, 5-7 minutes.
Add Flour, salt, and pepper and stir to coat.
Add water, broth, and milk. Stir. Bring soup to a low simmer. Allow soup to simmer uncovered for 5 minutes.
Add the cheese to soup. Stir to help the cheese melt and soup thicken. Serve.