Slaw? Grated broccoli with salad dressing as a minimum. Yes raw but a bit different.
Yes, I'm not too keen on raw broccoli either, but if I run it through my food processor slicing blast, I end up with thin shavings (mandolin would work fine, too) I makes an amazing slaw. The texture change makes a big difference. I then put a vinaigrette, chopped nuts, sesame seeds, dried fruit such as cherries, raisins, or craisins, sleep fed green onions. It's delish; I can eat a huge bowl. Great with a mix of broccoli and cauliflower, too.
I also throw chopped broccoli into pasta water during the last 4 minutes or so of cooking and then eat it with the pasta. I really like it with julienned carrots and peanut sauce.
Roasted is always my fallback, though.