My chickens have figured out that they can eat their own eggs, so they crack one and end up getting the other eggs dirty.
Most chickens will eat an egg that is already open. Soft shelled eggs, broken eggs, such as that. I do not consider them an egg eater. An egg eater is a chicken that purposely opens an egg to eat it. The others may join in to help eat it once the egg is open.
Have you actually seen a hen opening an egg? Could it be possible that one is laying a soft or really thin-shelled egg that gets broken when they walk on and off the nest? If egg shells are left, are they reasonably thick or are they really thin?
I don't know if you have one that is opening the eggs or if several are. It can be a learned behavior. I'd try very hard to determine which one or ones are actually opening the eggs and remove them to see if the others have learned. That would be my top priority, see how big of a problem you actually have.
The only two things I know of for sure to stop egg eating are to get them all to use rollaway nests (which isn't always easy) or to get rid of the hen or hens. I've read posts where people try the mustard in an egg, ceramic eggs, or dark curtained nests. On the few that actually give feedback once their hens have started egg eating, some say they worked, some say they did not. There is nothing wrong with trying any of these, they might work.
I don't think egg eating has anything to do with protein, calcium, or boredom. I think one learns that they can eat an egg after they find one broken or a soft shelled one breaks and they make that connection. They don't always make that connection when they find a broken egg, from what I've seen they seldom do. But some do.
I've only had one actual egg eater, one that would open eggs on purpose. She would open one or two eggs a day, no more, and a few of the others would help her eat them. As soon as I found out which one was doing it (she opened an egg in front of me) I ate her. One of my goals with chickens is for meat so that was an easy decision for me. It's not for a lot of people. About the time she started egg eating, I had a pullet just starting to lay that was laying from the roost at night and the eggs were breaking when they hit the coop floor. I'm confident that is where she learned. None of the others learned from her.