You might be overcooking it. Once the cell walls rupture too much, the sulfur compounds spread out and start to overpower the rest of the vegetable. It should still be somewhat firm/crisp when you bite into it.

You might also be using broccoli that’s had too many of the cell walls ruptured from processing before cooking. If you’re cutting with a dull knife, especially into small pieces, or smashing it somehow before cooking, those smells will leak out a bit faster.

Or, if you’re cooking from frozen, the ice crystals might have mushed up the vegetable.

Here’s the two main ways I cook broccoli:

Blanched: cut broccoli into big florets, big enough to constitute two big bites. Boil a lot of water, salted to about 2% salinity. Once it’s a rolling boil, put the broccoli in, and set a timer for 4 minutes. As soon as the timer goes off, dump the broccoli into a strainer and run cold water over it, or dunk it in ice water, to stop the cooking process. Serve and eat.

Roasted: cut broccoli into big florets. Toss in oil, and season with salt and pepper. Preheat oven with a sheet pan in it, to 450°F. Once preheated, take the broccoli and place it in a single layer on the sheet pan. It should sizzle. Roast for about 15-20 minutes, optionally flipping once (better char if you don’t flip it, but it’s only on one side).

Optional seasonings: garlic, pepper, red pepper flakes, lemon juice, honey, bread crumbs, pine nuts, any combination of the above. Works with either blanched or roasted.