Just imagine, for a minute, what it must feel like to be a broccoli stem. You spend your entire existence struggling to crown yourself in flowers, only to have the crown become the sole object of appreciation, taking all the glory for itself. Your beautiful florets are stolen from you, destined to become part of some exalted culinary creation, and you, sad stalk, are tossed in the trash. It hurts. Real bad. Deep, deep down.
But it doesn't have to be that way, nor should it. Broccoli stems deserve some attention of their own, which means that if you're one of those people in the habit of throwing them away, you might want to rethink that.
There's a lot you can do with broccoli stalks. It helps to think of them like kohlrabi, which is nothing if not a large, bulbous stem of broccoli. Kohlrabi is good both raw and cooked, with a mild flavor and a crisp, juicy center—and the same goes for broccoli stems.
You'll want to start by determining just how tough their exteriors are, peeling them off if they've grown too wooden with time. After that, you can decide what to do with them. If you have enough, you can cut them into batons or slices and sauté them in a hot pan with smoking oil, driving enough heat into their surfaces to get some browned spots.
You could also pickle them in a brine, like the one I use in this Quick-Pickled Asparagus recipe. It'll work just as well with broccoli stems. (And, of course, you can play with the flavorings, using different herbs or omitting them, et cetera.)
In all honesty, though, I rarely make such a fuss. Most of the time, I prefer to eat the broccoli stems raw, either tossed into a salad or arranged on a plate and drizzled with some olive oil and a sprinkling of flaky sea salt. They don't need much else. It makes for a fun little predinner snack for the cook—just a treat, nothing that will ruin your appetite.
And, if you happen to be making a platter of crudités, I implore you to include broccoli stems among the vegetable selection. Frankly, they're far superior to those awful raw florets, which get too much of the glory as it is—let's not heap on even more that they don't deserve.