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I finally figured out what to do with broccoli stems. For years I've been cutting off the florets and using that for dinner then I would put the stems in a bag awaiting a soup process. Now there is such a thing as broccoli slaw.
(Cousin to cole slaw). You grate the broccoli stems on a grater, 2 carrots and red cabbage. Then you add 4 tablespoons of vegennaise, squeeze a half of lemon and about 1/8 teaspoon of honey, maple syrup or agave. (Your choice, everyone is different). The lemon will make the Vegennaise liquidy. Then you take that and mix it into the broccoli slaw. It's a wonderful way to make a different kind of salad. By the way, no need to cook.