Couple of things - game cam set up in the chicken house. Or you can do what I did before I got the game camera. At night I would go to the chicken coop and catch a couple of hens, place them in an old rabbit hutch I had. If I had broke, cracked eggs the next day I knew it was not them. Put a red (or whatever color) zip tie around one of their legs and put them back into the pen. I kept doing that until I went through all the hens until I discovered it was not the hens or the rooster. It was a dang mouse who had built a nest under the nest box, chewed a hole through the bottom and was eating my eggs.
About a year later I did the same thing to discover that I had a young rooster who was eating eggs. He sure did make good stew.
Edited to add: the mouse did not eat the shells. The hens apparently cleaned that part up after the mouse cracked the egg and lapped up all the goodie. But on occasion I would find the egg shell squashed up in the bottom of the nest box. I also found a few eggs on occasion that had a small hole in them. I guess I got there before the mouse had time to finish getting the egg cracked open.