How to hard boil an egg and peel it without it breaking up or the white sticking to the shell?

Put eggs in a pan just big enough to hold them in a single layer cover them with cold water and bring them to a rolling boil. Cook for one minute, then remove them from the heat. Let sit for like 20 minutes (until you can put your hand in the water and not be too warm.)

Put eggs in pot, add enough water to cover eggs completely, and bring water to rolling boil. Turn off heat, cover the pot tightly and set aside for 30 minutes. They will be easy to peel. If you peel them under a little cold running water, the shells will most likely just fall off of the eggs due to the running water.

Another method that works is to add a splash of vineger to the water before boiling and cooking for about 3 minutes under med-hi heat.

Peel immedietly then, the longer they sit after that the harder they get.