Heads of broccoli are composed of the florets on top and their stems- the stalks. The stalks are thick and woody. If you want to serve them, you have to peel them back enough to expose the more tender stalk beneath . My older grand daughter only likes the stalks; so I often make them for her. Otherwise, I freeze them for future vegetable stock.
You can roast broccoli and enjoy a delicious crisp dark green vegetable; or steam it and enjoy the bright green color.