If possible, use eggs that have spent at least 1 night in the refrigerator. Remove and let them warm to room temperature.
Bring sufficient water to a boil and add room temperature eggs to the water using a tablespoon so as not to crack them.
Boil eggs 15 to 20 minutes vigorously.
Drain water from the eggs in a sink and, with the lid of the container held on, bounce the eggs like one would while popping corn with sufficient force to crack the eggshells. Remove the lid, and immediately flush cold tap water over the eggs. Peel and be surprised how easily they peel without breaking the whites.