Watch the time with hard-cooked eggs
Since eggs shouldn’t be cooked at a hard boil, egg experts prefer the term “hard-cooked” over “hard-boiled.” Whatever you call them, there are two problems you’ll want to avoid: cracked shells and the ugly green layer that can form around the yolk. For perfect cooking, start with eggs that don’t have any visible cracks. If they’ve been refrigerated, warm the eggs for four to five minutes in hot tap water. By bringing them to room temperature, they’re much less likely to crack in the hot water. In case small cracks do develop, add salt to the cooking water. The salt will help to speed up the denaturing of the egg white, causing less of it to feather into the water. Use at least a tablespoon of table salt per two quarts of water.
When hard-cooking eggs, watch the time carefully. Overcooking causes a green layer to form around the yolk. This layer is caused by a reaction between the iron in the yolk and the sulfur in the white. Heat speeds up this reaction, so the longer your eggs cook, the greater the chance of discoloration. I arrange my eggs in one layer and add cold water to cover them by an inch and a half. I partially cover the pot, and when the water has reached a full rolling boil, I turn the heat down to low, completely cover the pan, and let the eggs cook for thirty seconds. Then I remove them from the heat and let them sit in the hot water for fifteen minutes. I then put them in a bowl of heavily iced water for five minutes to further prevent overcooking.
Older eggs are easier to peel. The higher pH of an older egg makes the shell come off easier. That’s why I don’t recommend, as some cooks do, adding vinegar to the cooking water, since it would reduce the natural alkalinity of the slightly older eggs.