Basics of Peeling Hard-Cooked Eggs
According to the American Egg Board, the fresher the egg, the harder it is to peel. To guarantee hard-cooked eggs will peel easily, buy or store them a week or two in advance of cooking. It also helps to pierce the large end of the shell with a pin before cooking.
After cooking, cool the eggs promptly in cold running water. Tap the shell gently on the countertop. Roll the egg between your hands and remove the peel while holding the egg under running water.