The big supermarket eggs come from production reds, a strain of Isa Brown, but they need a fully controlled diet with 20 hours light per day to do it.
It's also why egg binding is common in production birds. The exact same amount of calcium is released from the shell gland to coat the egg, no matter what the size. So the bigger the egg the thinner the shell. Eventually one is ruptured in the chamber and that is usually the beginning of the end.