Mystery Egg Episode 2 - (Ren may choose to avert her eyes at this point.)
The prevailing theory from the Chicken Forum is as follows;
There is a phenomenon called Fairy Egg, where a temporary glitch in one of the stages of egg formation will cause a tiny yolkless egg to be laid. Many of the forum knew of it, but none has seen it.
That little pearlescent sac in my first picture may have been destined to be a Fairy Egg, but before a shell could form it was enveloped by the yolk and white of the egg further up the production line. Then a normal shell was deposited around the combination.
Out of curiosity I dissected the sac, which was a membrane enclosing thick eggwhite and a little "jellybean" which seemed to be just semi-solid albumen. No indication of disease or trauma.
Plain Jane the Plymouth Rock is laying normal eggs, and Flopsymopsy gets the award for her answer, "an egg inside an egg." As far as I can tell.
I apologise if this has put you off your Easter eggs!