What is the egg coated with?

Bob, I agree, the shell does not coat the egg. The bloom or cuticle coats the egg.

lf I accidentally crack a piece of egg shell into my eggs and eat it. It makes me gag.

the bloom actually coats the egg. It's the final coating the bird puts on the egg to keep bacteria from getting into the egg. I didn't say what kind of egg either.

The egg is not coated with shell. The shell is part of the egg.