Hard-boiled eggs are the original fast-food: high protein, high fat, easy to carry, non-polluting package (the shell). An easy-to-peel hard-boiled egg is the ultimate modern convenience food. But when the shell sticks and big chunks of the white are stuck to the shell, it's aggravating. And if you've carefully sourced your eggs directly from a farm producing eggs from pasture-raised organic hens, you could be paying $6 to $8 per dozen, making the annoyance a significant waste.
My favorite cooking magazine for the last twenty years has been Cook's Illustrated. Their most recent issue did a beautiful characterization experiment checking all the rumors you've heard. The short of it? It's all in the heating step.
Here's how we boil our eggs at Kookoolan Farms: Put the eggs in the pot, and fill with water to cover all the eggs. Any number of eggs and any size pot is fine. Now remove the eggs so you just have the water in the pot. Bring the water to a boil (this way, with the eggs _not_ in the pan, (1) you will add the eggs to hot water, and (2) you will be able to know exactly when to start the timer). When the water is boiling, turn off the heat so that the eggs are not violently jostled around and cracked during this step. With a slotted spoon, gently place the eggs into the pan -- it's crucial that they be heated abruptly, not gradually.
Watching closely, bring the water back to a boil; this will take less than a minute. As soon as the water returns to the boil, reduce the heat so the eggs are barely simmering, and set your timer for 12 minutes. After 12 minutes, drain the boiling water and immediately plunge the hot eggs into the coldest water you can: ice water is best. Note: 12 minutes is for standard large eggs. For medium or small eggs, use 11 minutes. For jumbo, extra-large, or duck eggs, use 13 minutes.
The very rapid heating shocks the shell and its membrane away from the whites, and all the eggs will slip easily out from their shells! The very rapid cooling stops the cooking process so the eggs do not overcook. Tender whites, creamy yolk, no green margin, and easy to peel -- every time!