Via Simply Recipes
To get hard boiled eggs that are easy to peel, make sure they are several days old. Hard boiling farm fresh eggs will usually be difficult to peel. If you need to hard cook fresh eggs, and want them easy to peel, steaming the eggs works well. Here are tips for how to boil eggs so they come out perfectly every time:
1 Put the eggs in a single layer in a saucepan, covered by at least an inch or two of cold water. Starting with cold water and gently bringing the eggs to a boil will help keep them from cracking. Adding a tablespoon of vinegar to the water will help keep the egg whites from running out of any eggs that happen to crack while cooking. Adding a half teaspoon of salt is thought to help both with the preventing of cracking and making the eggs easier to peel. Put the burner on high and bring the eggs to a boil. As soon as the water starts to boil, remove the pan from the heat for a few seconds.
2 Reduce the heat to low, return the pan to the burner. Let simmer for one minute. If you are using an electric stove with a coil element, you can just turn off the heat. There is enough residual heat in the coil to keep the eggs simmering for a minute.)
3 After a minute, remove the pan from the heat, cover, and let sit for 12 minutes. The eggs should be done perfectly at 10 minutes, but sometimes, depending on the shape of the pan, the size of the eggs, the number of eggs compared to the amount of water, and how cooked you like them, it can take a few minutes more.
4 Either remove the eggs with a slotted spoon and place them into a bowl of ice water (this is if you have a lot of eggs) OR strain out the water from the pan, fill the pan with cold water, strain again, fill again, until the eggs cool down a bit. Once cooled, strain the water from the eggs. Store the eggs in a covered container (eggs can release odors) in the refrigerator. They should be eaten within 5 days.