It dove over, and broke the rear brake lever. The same one I broke on NY day

Anyway, it's a cheap part, and I replaced it last time. However it was a pain in the butt, which means I'm doing it wrong.
last time, I didn't take much of the headset apart, grew frustrated, then just muscled the cable out with some needlenose. Done.
I'm confident there is a 'correct' procedure, so I thought I'd ask before I did the front brake ride of shame to the shop

Thanks!