What to do with broccoli stalk?
Just slice it into thin discs (a mandoline is quick) and the kids use it as chips'n'dip. Try some natural or Greek style yoghurt and whole seed mustard as a dip. Very crunchy and tasty

If the skin is dry or blotchy I quickly run the potato peeler over it first

Otherwise, just grating it into soups or stews is a nice vegetable filler

EDIT Doh, forgot the best thing to use it for Coleslaw, it replaces cabbage perfectly. Or you can mix cabbage and broccoli. Just coarse grate it with some carrot, onion. Blend it up with a little mayo and yoghurt, or lemon juice and olive oil. Add some ground fennel and cumin seeds or some chopped mint for extra zing