In a large saucepan over medium heat, cook onions in olive oil until translucent. Add in broccoli and peeled potatoes and cook until vegetables begin to release their juices. Pour in chicken or vegetable stock, to cover all the vegetables. Bring to a boil, then reduce heat and simmer until vegetables are tender for about 15 minutes. Remove from heat and let cool slightly. Stir in cheese until melted.
Place all in a blender, season to taste and serve.
You can add more crumbled cheese or croutons to the top just before serving.