You can badmouth broccoli all you like, but the fact is that it's everywhere, it's cheap, it's got more character than almost anything, it's good for you, and it's in season.
It also tastes good, if you start with a decent specimen and treat it right. The "decent specimen" part shouldn't be that difficult. Needless to say, if you have access to something from a garden or farm near you, that's ideal. Otherwise, just look for dark (no yellow), tight flowerheads. Size doesn't matter. Cook it sooner rather than later. Period.
Like asparagus, broccoli, or at least all but the youngest, tenderest broccoli (if you're not a gardener, you'll never see this), is best peeled. I know you probably haven't done this before, and I know it sounds like a pain in the neck, but it's only a five-minute pain in the neck, and it's going to remove the single most objectionable element of most broccoli: its toughness. Just use a vegetable peeler or a sharp knife to remove the thickest part of the skin, which is mostly running along the main stalk; you'll immediately see the color change from dull green-gray to bright -- appealing! -- green. You can do the same thing along the minor stalks too, but it's more of a hassle.
On to cooking. And it can be as simple as this: Bring a pot of water to the boil and salt it. Cut the broccoli along its stems, so you have roughly equal-size lengths, each of which has a floret or two on top. Boil for six or seven minutes, until the stalks are tender but the flowers are still bright green. Drain, then either serve immediately, or run under cold water or (even better) plunge into a bowl of ice water. (Chefs call this "shocking")
If you're serving the broccoli right away, you just dress it with olive oil and/or lemon, or soy sauce (lemon is good here, too), or butter, or vinaigrette, or whatever other dressing you like -- neither ketchup nor barbecue sauce nor mayonnaise is unheard of, and whatever makes you happy is fine.
But the ice-water treatment is what makes broccoli (and many other vegetables) super-useful. Once the broccoli is cool, you can drain it again, and refrigerate it for days. Without further ado, you can eat it cold or at room temperature (a little better, I think) -- again, dressed simply.
You'll see the real benefit of precooked broccoli, however, when you have five minutes before your next meal. You heat some olive oil in a pan (yes, of course you can use butter). You throw in maybe a dried chile, some slivered garlic, or a chopped onion, and you warm the broccoli in that. It's done while you're doing five other things. You serve it hot or at room temperature.
Or: You take that precooked broccoli. You toss it with garlic, oil, and cooked pasta -- there's a recipe here -- and you have one of the single best vegetarian (vegan, even, though I have to mention that a little prosciutto goes a long way in here), healthy, practically one-pot, fast pasta dishes there is. (It works, too, with cauliflower, broccoli rabe, collard greens, kale, and other dark greens.)
But there are many other ways to cook broccoli, even without the parboiling technique. One is a beef and broccoli stir-fry, using a technique which steams the broccoli in the skillet or wok, by which you avoid a common mistake home cooks make when stir-frying: winding up with too-crisp vegetables. (It's almost impossible to get broccoli tender enough by stir-frying without some liquid.) If this doesn't make the broccoli-haters happy, I give up.
But it will.