To make easy-to-peel hard-boiled eggs, use eggs that are at least a week old, and crack the shells slightly just after they're done cooking. Place the cracked eggs in an ice-water bath for five minutes and the shells should peel off smoothly without much difficulty.
It is essential to use eggs that are about seven to 10 days old to make hard-boiled eggs that are easy to peel. Fresher hard-boiled eggs are tougher to peel because the membranes underneath the shell tend to stick to the egg whites, while the membranes are looser in older eggs.
To cook the eggs, place them in a saucepan covered with at least 2 inches of water, and place on the stove to boil. Turn the heat off once the water comes to a full boil, cover the saucepan, and let the eggs sit in the hot water for several minutes. For large eggs, let them sit for 12 to 13 minutes. Set a timer to avoid overcooking the eggs.
Drain the hot water immediately, and roll the eggs around in the dry saucepan to crack them slightly all over. Transfer the eggs to a bowl of ice water for five minutes. The cracks allow the ice water to get into the eggs faster, stopping the cooking process and further loosening the membranes from the egg whites. The egg shells should come off smoothly in large pieces.