No matter which method you use to boil the eggs, to stop them from overcooking, transfer them to a large bowl of ice water to halt the cooking process and cool them down enough to handle (about 4-5 minutes).
Remove the egg from the ice bath and create a single crack in the shell, either by tapping it against a surface or with a knife or spoon.Don't be too rough otherwise, you can cause the egg white to crack, too.
Roll the cracked egg lightly back and forth on a hard surface (like a cutting board or your kitchen counter) with the palm of your hand.This will cause fractures across the entire shell, making it easy to remove. Don't use too much pressure, or you risk breaking the egg white too.
At this point, the fractured shells should be fairly easy to peel away from the egg white. I usually start peeling from the large end of the egg (where the air bubble is).You can do it under running water (or in a bowl of water) to make it even easier and remove any small shell pieces. Voila- easily peel hard-boiled eggs!
Notes
Generally speaking, for the easiest peel hard-boiled eggs, it's recommended that you use slightly older eggs that have been in your fridge for a few days vs. fresh eggs. This is because the shell membrane won't be quite as "sticky" at that point.