Do I start with two lbs of broccoli and just use florets, or should I be using the stalks, too?

As long as you peel them, they taste just as good as the rest of the vegetable. Actually, they'd be perfect for this particular recipe considering the long cooking time. They will add body to your soup.
Personally, I'd make the stalks (upper and lower stalks) the bulk of the soup, hold back the florets and roast them hard to serve as a textural garnish along with the cheese. When caramelized and slightly charred, broccoli florets have such a great, nutty flavor.

It's a closely guarded secret that the stems have the sweetest flavor, so I recommend using them!

You can use the stalks too, If you like - the soup will just be a bit thicker, but you can always add more liquid!