Turns out it was an egg-within-an-egg!
inside egg was normal in all respects except for that it was a
soft-shelled egg--not hard-shelled like normal. It had gotten another
coating of albumen & membrane in addition to it's second shell. These egg-in-an-egg oddities occur
when an egg hangs around in the hen's system a bit too long and and get a
double shellacking in the shell department.
The kid was properly intrigued/disgusted at the same time.