In a pot (4 quarts or larger) saute ground beef and onions until browned.
Add salt, pepper, diced green bell pepper and garlic. Saute for 30 - 60 seconds.
Add potato cubes and beef broth. turn heat to high and bring to a boil. Cook until potatoes begin to soften (about 10 minutes).
Once potatoes have softened (but are not cooked all the way-they will finish cooking after adding remaining ingredients) add flour rue. Whisk to avoid lumps. As butter melts the flour will begin to thicken the soup.
Last, add the milk and shredded cheese. Stir until cheese is melted.
Serve with garlic bread or toast.