I like to use the stalks of my broccoli. I just peel off the outer layer with a veggie peelers and then chop them small so they cook evenly with the florets. The stalks have great flavor and it's so much waste if you just throw them away.
This soup was very tasty. The broccoli was slightly crisp and the corn and potatoes gave it a great texture. I picked up a loaf of fresh rosemary bread and it was so good dipped in the broth. I would make this again and maybe next time try adding some cauliflower. I think that would go well with the broccoli.
Recipe is from Marthastewart.com