Melt the butter in a large saucepan over a medium heat. Peel and roughly chop the onion. Add to the pan and cook for 2-3 minutes, until starting to soften.
Roughly chop the stalks of the broccoli. Chop the potato (no need to peel). Add both to the pan and cook for another 2-3 minutes.
Pour in the stock. Chop the rest of the broccoli into small florets and add to the pan. Cook for 15-20 minutes until the broccoli is soft.
Use a stick blender to blend the soup until smooth. Add the cheese and cream: stir. Taste to check the seasoning and add salt and pepper as needed.