I've still got leftover soup from when my brother came over to cook, so had some for lunch today. This pureed vegetable soup starts with a mirepoix. You saute that until the onions become clear. Then you add vegetable stock and small dice potatoes and cook until all vegetables are tender.
I lose the thread after this, because there was also some egg yolk/milk mixture that gets added and I can't remember exactly what herbs and spices went in. I think we steamed the broccoli florets separately. Anyway, you can certainly improvise with standard herbs and spices in the broth mixture. Once the potatoes are cooked, you put the soup into a blender or food processor and puree until smooth.
Return the pureed soup to the pot and add in the steamed broccoli. Heat for a few minutes and serve. Season to taste. You could also add some shredded cheddar or some goat cheese to this.