Peel and dice the onion and potato and sautee them in a bit of olive oil over medium heat.
Once potatoes and onion are soft, add a litre of vegetable stock. After about 10 minutes, chop the brocolli head into small pieces and add to the soup and let it simmer for another 10 minutes.
Break the Stilton into small piece and add roughly half of it to the soup, keeping the rest for later. After the cheese has melted into the soup, use a blender to smooth it all out. Put it back on the hob for a couple of minutes, before seasoning it (see tips). Now you are ready to serve it into bowls.
Once in the bowl, add some crumbled cheese on top. Break up some french bread, butter it, and serve it along with the soup.
Vegetable stock is quite salty as it is, so no need for extra salt. However, pepper is a nice addition. Any blue cheese will do, but stilton does go very nice with it. For an extra edge (although possible cheese overkill) use cheese spread instead of butter on your french bread.