To hard-cook eggs, add water to a large saucepan and place the desired number of eggs in a single layer in the saucepan. Make sure you have enough water to measure at least 1 inch above the eggs. Bring the water to a boil, stirring the eggs gently when the water begins to simmer. This will help center the egg yolks. When the water reaches a full boil, cover and remove the saucepan from the heat. Let the eggs stand in the hot water, covered, for 15 minutes if you are using large eggs. Increase the time to 18 minutes for extra-large eggs; decrease to 12 minutes for small eggs.
Pour off the water and immediately run cold water over the eggs. This helps prevent the eggs from overcooking. If the eggs are overcooked, there may be a reaction between the iron in the yolk and the sulfur in the white, and a greenish ring will form around the cooked yolk. Let the eggs stand in the cold water until they are completely cooled.
To remove the shell, gently tap the egg all over, roll between your hands to loosen the shell, then hold the egg under cold running water as you peel off the shell. The fresher the eggs, the more the shell membranes cling to the shells, so we recommend buying and refrigerating eggs a week to 10 days in advance of hard cooking. This allows the eggs to take in air, which helps separate the membranes from the shell. A hard-cooked egg should have both a firm white and a firm yolk and no greenish ring around the yolk.