The key for easy-to-peel eggs as I have found is to start cooking with boiling water for about 1 minute. The high temperature will cook the outer part of the egg really fast, thus prevent it from sticking to the thin film between the shell and the egg. After 1 minute, you can adjust the temperature to achieve your desired doneness. Also, when you peel, try to roll the egg gently over a hard surface to break the shell into small pieces and to detach the shell and the film from the egg. Doing that extra step will help you to peel the egg not only easier but also much faster.