As always I found your question very intriguing, I found the below link and I hope it helps. They did say it's a hard habit to break once they start.
Does anyone have any experience with chickens that eat their own eggs? And do you know then what to do about it?
We called my cousin, and she said "chicken stew." However these are pets, Sophie and Charlotte, and they are the matriarchs of the prairie, here...plus they are quite old...
So chicken dumplings is out of the question, rather we are needing chicken therapy?
Yes, chickens will eat their own eggs. When I raised chickens, I often would break a couple that were cracked or small on the floor for them....I also took this as a sign that they needed some oyster shell in their scratch feed!
You need a big Rooster to come in and take care of business ! LOL
Take the eggs away as soon as possible and try to get another chicken to 'foster them'
My husband was brought up on a farm and he said they do that.