Thanks for the advice. We lock her out of the coop for a couple hours at a time twice a day to make sure she is eating and drinking, but we will remove the eggs as well. The 7 other hens lay at different times of the day, ranging from 7am to 5pm, and they prefer to lay in their nest boxes, so we don't want to lock all of them out of the coop. We'll find something that gets her out of her broody mood until next spring when we want to hatch our own chicks, maybe even moving her to a different cage.
I also see the resemblance with the Blue Orpington and the Blue Ranger.