I had one hen that was consistently broody. Absolutely awesome mom. Loved her. She would go broody, raise the chicks for a few months while laying again, and then go broody all over again.
I usually let her set for a few weeks in the breed pen to make sure she was setting "for real". Then at night after about two weeks I would move her into a cage so the fire ants couldn't get to the eggs and chicks when they hatched. She once sat through a storm that ripped the roof off the hen house she was sitting in and rolled cages and hutches around the yard. (Oddly that was the first and only time my Bobwhite Quail ever layed too?) She did a great job covering eggs, and usually hatched out everything you put under her. I even coordinated my incubators inside to hatch when she would so I could foster the babies on her. I loved checking on her and seeing her covered in babies. She always looked like she was so happy.
She would even steal chicks from other hens to take as her own. I made the mistake of letting one of my Rhode Island Reds sit once. Apparently she hatched out two chicks during the night and decided she was done. When I went to check on her the next morning the two chicks were in the middle of the yard screaming their heads off. Periodically she would run over to them and rap them sharply on the head. The Faverolle pen was next to theirs and Monica was just frantic to get to the babies. She had broken the feathers on her chest rubbing the wire, pacing trying to get to them. Upon rescuing them I discovered the RIR had scalped the babies and they were covered in fire ants. I doctored them and gave them to the Salmon Faverolle. Monica immediately stuffed them under her and proceeded to take care of them with the month old brood she already had. Unfortunately the babies didn't make it, but we tried.
I would love to have another hen like her when I get chickens again.