I can never spell it either. I have no excuses - it's my favourite vegetable also, and it's also spelt the same in French, so I'm pretty much stuck either way.
"Brocco-lie" is a very common pronunciation in Leicester. And it drives me up the wall. That and "straight-the-way" instead of "straightaway". Arrgghh!
It's Britons. People from that island are called Britons. Not Brits - that was a word invented by lazy tabloid journalists and it makes me cringe everytime I hear it.