Hi, I love broccoli, and grow a lot of it, and there are tons of cabbage moths here. Personally, I find no issues with picking the eggs/larvae off the plants manually. They're hard to spot at first, but once you get used to it, it's pretty easy. I like to spend a lot of time inspecting my plants anyway, so I just rub the eggs off the undersides of the leaves while I do that, and keep an eye out for the holes that indicate a larva has hatched, and when I see that, hunt it down. This works for me.
If it doesn't work for you, the best thing to do is row covers to keep the moths from laying their eggs on your plants: