In a large stock pot saute onion in butter. Add potatoes, water and bouillon cubes. Cover, bring to boil and then reduce heat to medium and cook until potatoes are tender, about 15 minutes.
Remove tough outer skin of broccoli stems and cook broccoli. Once cooked add to soup.
In a blender or food processor puree half of the soup and return to stock pot. Season with salt and pepper.
Add cheese and heat soup through until cheese is melted. Serve warm.
