Hen laying soft-shelled eggs

Ginger, a one year old Black Copper Maran, has periodically been laying strange looking eggs. What caught my attention were two recent ones with papery soft shells. Some of her eggs also have some whitish areas on the shell. After looking this up, it seems that it is a sign of an unbalanced diet lacking in calcium and protein.

This makes sense, as I rarely see Ginger eating the regular chicken feed (pellets and oyster shell). In fact, she is a real hog of kitchen scraps and often chases the other chickens away if we put something out. We used to think it was kind of funny -- Ginger knew how to work the system and get the good stuff. But it seems to be a problem, especially since we throw out a lot of bread and vegetable scraps that would be low in protein and calcium.

Our solution right now is to separate her for a while and only give her access to the regular pellets and oyster shell. We'll wait to throw any scraps out to the other chickens when Ginger is in her own cage. We'll try this for a little while. I'd hope we could throw out bread, etc. without one chicken eating it all.