I know that this has been covered before. However, I believe that I've recognized the ultimate technique for peeling a cooked egg, be it hard or soft boiled. Let me try to explain how I was able to perfectly peel two dozen eggs that were cooked up for Easter Sunday.
Previously, I'd been taught to crack the eggshells while the eggs were piping hot, then immerse them into very cold water for a few minutes. This has always worked for me. But what about cooked and colored eggs that were refrigerated, how do you get the shells off of those?
What I did was to crack the shells on a flat, hard surface, so as not to break the egg white. I gently hit the table with the egg, all over the place, turning it a little as I continued to crack the shell. When the shell was crazed, I gently applied pressure between my fingers and thumb, as I had noticed that by so doing, it caused the shell to lift away from the egg. I did this all around the egg, watching the shell fragments, still attached to the membrane, lift away from the elastic egg white. Then, with the side of my thumb, I began to lift the shell fragments away from the cooked egg, taking care to capture the membrane. In most instances, the membrane lifted the egg shells as I peeled the egg.
This method works because the egg shell won't flex, while the egg white does. As the pressure is applied to small areas of the white, it deforms the egg. The rigid shell has either to crack again, to follow the white, or lift away. Fortunately, the shell is strong enough to resist cracking, and simply separates from the white. When this has been done all over the egg, you can easily peel away the egg shell.
Hope this helps all of you who have a miserable time peeling eggs.
Seeeeeeeya; Chief Longwind of the North