Boiling an egg is an easy process, but if you ask 10 people how to make hard-boiled eggs, they will all give you a different answer. I don't boil just one egg at a time, but you can if you want or need. I usually do at least six. They seem to last quite a while in the refrigerator but they don't make it longer than one week at my house. Take a small sauce pot and gently set in six eggs, be careful not to break any of the shells, and cover with cold water. Put the pot on the stove and turn to high. Bring pot to a boil, and then reduce heat to a low boil and let cook for 11 minutes. Turn the heat off. At this point I usually let it sit in the hot water for one minute. If you're worried that the eggs are not cooked enough at this point, you can take one of the eggs out of the pot with a slotted spoon. Then you can hold the egg under cold running water to chill outside just enough to handle so you can peel it. Then take the egg and cut it open and take a peek inside. It will be done. Whether the egg is done or not at this point you are obligated to eat this egg. Add a little salt, pepper, hot sauce, horseradish or whatever you like. When you are sure that your eggs are done place the pot into the sink and run cold water in it. Once the water in the pot is cold to the touch,The eggs will probably still be warm in the middle and that heat will radiate out and change the temperature of the water. I usually put the eggs, pot and water all into the refrigerator at this time and let chill. You can speed the cooling process by putting ice in the cold water.
Some people will tell you to put salt or vinegar and water, but I don't use either. I don't think it makes any difference. But if that is your preference, feel free to put that in the water if you think it does any good. If you are cooking organic eggs you will probably notice that they are a little harder to peel than a regular egg, but don't let it be a dealbreaker for you.