Fish them out, put them in a large bowl and let them cool a little bit before you use your hands to remove all the skin and bones. Put the chicken meat in the fridge until you want to use it. At this point, you have achieved broth. You have resisted your urge to stir. You can let it cook longer if you want.
Several hours is fine.
When you decide you're finished, all you have to do is strain the broth. There are many ways. Technically, you're supposed to use unused cheesecloth, but I never have. If you have a large strainer or fine sieve, just dump it through that, slowly, into a big bowl. If you don't have a strainer, you can wet a thin kitchen towel that you don't care about.