Spice girls sounds like a scientist like me

we are problem solvers....our brains just wonder and work and then try things til we work it out.
I have a hen that lays an odd shaped egg, with excess calcium pimples all over, concentrated at the "small" end. She is a year or two old. First "egg" I ever got in my life was from her, layed in my garage(quarantine) from the perch onto the floor. It was soft shell and broken.
I don't really count it.
She is a bit of a freako. I picked her because I liked her lovely look. She was a spaz in the garage. She is better outside, but I'll bet you $1 If I tried to flip her out, soft shell next day. Also, free access to oyster shell. If I take the oyster shell away, soft egg it seems. I am going to be experimenting with the vitamin D, and other natural remedies.
She lays an extra large round blue egg 6 out of 7 days, I give calcium and good food an free range...she has it awesome! I'm not going to cull her, we happily eat her eggs. I just don't give hers out.
I would be curious to breed her, for our little flock experiment of course, just to see if her children lay a better egg, and proving that the shell gland was damaged somehow or if it was genetics.
So curious to find information on what(besides calcium) has worked for others!!!