A hard-boiled egg and a hard-cooked egg are the same thing -- eggs that have been cooked in the shell until the whites and yolks are solid. For cooking instructions, see How to Boil an Egg.
1. Refrigerate the Raw Eggs for a Week
Getting your eggs to peel easily starts with the eggs themselves. The fresher the eggs, the harder they are to peel. This is because as eggs age, they lose some of their carbon dioxide and become more alkaline, making them easier to peel. Consider purchasing your eggs 5 to 10 days before you plan to boil them. A little aging also helps the membrane separate from the shell in each egg. When cooking, do not add vinegar to the water since this can lower the alkalinity of the eggs.
2. Quick-Cool the Eggs
After draining the boiled eggs, cool completely under cold running water or in a bowl of ice water. This is an ideal time to peel the eggs. When the eggs cool they contract slightly in the shell, making them peel more easily.
3. Crack and Peel the Eggs
To peel, gently tap each egg on the counter and crack the shell all over. Rolling the egg on the counter or between your hands helps to loosen the shell. Start with the large end of the egg and peel the shell off with your fingers. Peeling the egg under cold running water also helps to remove the shell.
4. To Store Peeled Eggs
Once an egg is peeled, it should be eaten that day.