Fowl play

One of our hens has developed a very bad habit; she has begun eating eggs. We don't know which one it is so each one in turn must be put in solitary confinement to eliminate her from our enquiries, and she must remain there long enough for another crime to take place. This process is going to lose us a lot of eggs. Innocent hens are released back into the flock with a black indelible marker stripe along her beak. 
The internet tells us that the cure is to blow an egg and fill the shell with mustard. That is one idea, another idea is casserole.