Fun fact: Brocollis is the 'veg kids don't like' in Amercia mostly. Pixar even edited scenes in 'Inside Out' where a dad feeds his daughter broccoli, turing it into bell peppers for the asian market:
Broccoli, cauliflower, and green beans we (brother and I) were always fine with as kids. It was the asparagus and spinach I never cared for as a kid. Turned out it wasn't the spinach's fault, my mother would just buy bags of frozen spinach, put it in a microwave safe container and turn it on. So if tasted bad. As I learned to cook I started to like it as I actually used it in other ways. Asparagus though... I rarely give a chance, and usually if I do I'm frying it in bacon grease which defeats the purpose of eating a vegetable I feel.
Both my kids favorite veggie was broccoli when they were small. I'd prepare it the way you'd get it in an Italian restaurant - small parts of it just bleached for a short time, so it stays firm, served with nice olive oil and salt. (And a bit of lemon, if I have it on hand)
Broccoli (like so many veggies) tastes awful when overcooked into a soft and mushy consistency (and then it also changes its taste in a bad way).
Here in Germany grandmas typically are amazing cooks, with the sole exception when they cooked veggies. That generation loved their vegs really soft and overcooked.