I decided to give Lynn D.'s Marcella Hazan suggestion a try first, and found the recipe trolling the net on a UK site for a CSA there called "River Nene." This is what you need:
225g onion, thinly sliced
60g black greek olives, pitted (important to use nice olives)
4 flat anchovy fillets, roughly cut
50g fresh parmesan, cut into thin slivers
6 tbsp olive oil
225ml dry red wine
You cut the broccoli into florets, dividing the larger clusters in half. (ugh, don't usually care for that bit of the broccoli, but I did it.) Then you peel the stalks and cut them into long strips, about a 1/4 inch thick. In a sauté pan, or the like, make a thin layer of onion slices, and next a layer of broccoli stems. Dot with a few olives, some anchovy fillets and a few slivers of parmesan. Sprinkle with a bit of olive oil. Repeat, saving the broccoli florets for the last layer. Add the red wine, cover and cook for 1 hour (!) over a low heat or until all the wine has evaporated. Marcella says not to disturb it or stir, and to eat it straight away when it is done-reheating being a Bad Idea. Don't know why, and didn't try that. Ate it all up, with bread and a bit of goat cheese, for supper. (I made about 2/3 of the recipe, consistent with the amount of broccoli I had, and shared it with one other person.) I'll bet it would be just as nice at room temperature, though.
As you can see, this is not pretty. Doesn't look like a treat. But it is. I who shrink from broccoli, embrace it. Well, maybe not embrace, broccoli is not so huggable, despite the tree-like appearance. But I like it this way- a lot. Be advised, especially if you are, as I am, dubious about broccoli in general, that it is different from all prior broccoli recipes I've tried. Thank you, Lynn- a keeper.