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
cooking.stackexchange.com/users/3203/TFD
In the winter I use it to make broccoli cheese soup.
I actually think the heavy stem makes for a better texture than the tops (they get very mushy).
cooking.stackexchange.com/users/218/Satanicpuppy
Shave the stalk with a vegetable peeler and quarter it lengthwise.
I then use the quartered stalk pieces as a platform on which to set the florets for steaming.
The stalk pieces are immersed in the boiling water while the boiling water steams the florets, resulting in perfectly done florets and stalks after about 5 minutes or so.
cooking.stackexchange.com/users/990/Mike Yockey
When cooking the stalk, you should peel the outside first (just use a swivel peeler and take the outer skin off) before slicing it up.
The outer layer can be a bit tough.
Also, be sure to cut it fairly thin so it will cook at the same time as the florets.
cooking.stackexchange.com/users/2047/Bob
If I have a few of them knocking about I'll stickem into stock, either vegetable (along with carrot peelings, onions scraps and anything else that would go to waste (except potato skins which make your stock very cloudy), or chicken if I've got a carcass going spare.
cooking.stackexchange.com/users/2010/NBenatar
I have to confess, I tend to cut them into chunks and eat them raw, while cooking the rest of the dinner.
If you cut them into strips, I'm sure they'd make a good crunchy alternative to carrot/celery etc for dips.
Or, leave the broc whole, and stand it up in a narrow pan with enough water to cover most of the stem, and the lid on.
The florets steam, the stem boils, and you can eat the whole thing.
cooking.stackexchange.com/users/17240/Phil M Jones
Once peeled and sliced, they can be steamed, stir fried, or used in salads.
I've heard broccoli stems called the poor man's asparagus.
cooking.stackexchange.com/users/2491/Mark
You can peel them, dip in egg wash and then breadcrumbs and fry: really good vegetable chips
For a broccoli and cheese soup, I use Gordon Ramsey's recipe +
1/2 cup shredded cheddar cheese, peel the stems first, and chop very finely, it helps the stalks cook faster.
I reserve a few florets for garnish.
You can also use the stalks in place of asparagus.
Slice stalks asparagus shape, roast on high heat with a little olive oil/garlic powder.
Serve with hollandaise sauce.
Or you can use it like peas:
peel the stalks, blanch until just tender but still a little crisp.
Drain and mix with a little butter and LOTS of parmesan cheese and black pepper.
Also use in place of cabbage in a quick cole slaw, i use a vinaigrette rather than mayo and pair with bbq chicken sandwiches
cooking.stackexchange.com/users/18057/mkc
I like to peel them, cut them in cubes and fry them together with carrot cubes.
Once they're done, I flavor with a little pepper and salt
(not much).The real kicker is mixing some apple vinegar with sugar and pour that in the frying pan once the stuff is done.
Don't continue to heat now, that will make it loose
it's sourness.
Very delicious imho.
cooking.stackexchange.com/users/19867/Anpan
It is kind of annoying to buy broccoli and pay per weight when there's this huge and heavy stem, so I was wondering what I could do with it?  I know that it can be cut and steamed/cooked like the rest of the sprouts, but are there any specialities for it?
What to do with broccoli stalk?
cooking.stackexchange.com
<vegetables><broccoli>
cooking.stackexchange.com/questions/9581
cooking.stackexchange.com/users/2845/Patrick
Shave the stalk and cut it into slices or chunks to eat raw, or add to soups, stews, stocks and coleslaw. You will need to peel the outside before using it. Then you can either eat it raw or use it for soups.
Slice it and eat it raw with a dip. Use it for soups and stocks. Peel the outside before chopping.