1. Roughly chop onion, potatoes, celery and garlic. Cut broccoli into florets and chop stems.
2. Heat olive oil in a large saucepan over medium heat, and sauté onion, celery and garlic, for 5 minutes, stirring occasionally.
3. Add broccoli stems, chopped potatoes and broccoli florets.
4. Pour the stock. And salt, pepper and thyme. Bring to a boil, reduce the heat to low and simmer until al vegetables are tender, about 25-30 minutes.
5. With an immersion blender, puree the soup until smooth. Add heavy cream and stir. Check the seasoning and add salt and pepper if needed.
6. Simmer for 10 min and turn heat off.