I am absolutely no help as I have never seen anything like that! I am curious to what it is too. I am sure someone will come along soon and explain, I am sure.
My thought was that it was washed and then left a while, which gave time for the bacteria to get inside. But, I have never seen that before, so it is merely a guess.
the egg was hard boiled and it was refrigerated prior to use. it wasn't left out for an extended period of time and it wasn't washed and left out to sit. it went straight from the refrigerator into some boiling water for 6 minutes.
i had about 9 of these eggs over the course of a week and a half and they were all fine, but this one was weird. it had no blemishes on the outside of it at all. no spots or discoloration. it looked like all the other eggs, but the inside shell contained these dark spots.
I would ask the Avian Medical Center in our area (we are lucky they treat chickens!). If you don't have one try to get in touch with either the Dept. of Agriculture or a Veterinary College and ask who to email this photo to. Maybe if you know a chemistry professor at a college you could ask if they want to test it?
O.K. stupidchicken. It is mold. I laughed out loud when I read your second post.
What is the temp of your refridgerator? Were the eggs stored on the door where the temps are warmer? The mold grew after the eggs were boiled and cooled. If you look very closely you can the surface of the cooked egg has little dimples. This is where the mold has been feeding. The mold spores got in through small cracks in the shell that are exposed to the air. I bet if you peel that egg there won't be any mold growth where the shell is intact.