1. Peel potatoes and cut into cubes. 
2. In a saucepan, sauté onion in butter.
3. Add potatoes, water and bouillon cubes. 
4. Cover and bring to boil, then reduce heat to medium and cook until potatoes are tender, about 15 minutes.
5. Add broccoli, then process soup in a blender until smooth (or whatever consistency you desire). 
6. Season with salt and pepper to taste. 
7. Return soup to heat, adding cheese and heating until melted.

Serve.