Melt butter in a large skillet. Add onion and cook until tender but now brown. Stir in potato and stock and cook at a simmer until potato is completely cooked. Mash potato with a fork.
Stir in cheese. Bring soup to a simmer and stir until cheese is melted. Add broccoli, salt, pepper, and cream and heat thoroughly. Do not boil. Serve hot with a bit more shredded cheese sprinkled on top.
NOTE: If you like a smoother soup you may puree in a blender before serving.