Title: Hard Boiled Eggs
First make sure that you are using eggs that are several days old. If this is Easter time, and everyone is buying their eggs at the last minute, buy your eggs 5 days in advance of boiling. (See the reference to using old eggs in Harold McGee's On Food and Cooking). Hard boiling farm fresh eggs will invariably lead to eggs that are difficult to peel. If you have boiled a batch that are difficult to peel, try putting them in the refrigerator for a few days; they should be easier to peel then.
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, but some people find that the vinegar affects the taste. I don't have a problem with it and I usually add a little vinegar. 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.
Reduce the heat to low, return the pan to the burner. Let simmer for one minute. (Note I usually skip this step because I don't notice the eggs boiling until they've been boiling for at least a minute! Also, 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.)
After a minute, remove the pan from the heat, cover, and let sit for 12 minutes. If you are doing a large batch of eggs, after 10 minutes you can check for doneness by sacrificing one egg, removing it with a slotted spoon, running it under cold water, and cutting it open. If it isn't done, cook the other eggs a minute or two longer. 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. When you find the right time that works for you given your pan, the size of eggs you usually buy, the type of stove top you have, stick with it.
I also find that it is very hard to overcook eggs using this method. I can let the eggs sit, covered, for up to 15-20 minutes without the eggs getting overcooked.
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.