The non-broody, Mediterranean breeds have been being selected that way since the ancient Egyptians first figured out how to artificially incubate eggs. Other peoples used broody-breed bantams to incubate while their primary egg-laying breeds did their job -- lay eggs without taking months off to rear chicks.
I've only had two Brahmas before -- the Dark variety -- and both went broody in their second year. Noodle was so determined a broody that she managed to hide an egg and hatch it even while I was taking the eggs away from her.