My mother cooked eggs the way most Baby Boomer generation mothers did. She heated a pot of water, dropped in a couple of eggs with a thunk, and boiled the shit out of them.
Mom, I love you, but your hard-cooked eggs suck.
When protein reaches 170°F, it begins to toughen. When you drop cold eggs into rapidly boiling water and leave them for for 12 minutes, you'll get rubbery whites. You'll also get cracked shells and seeping goo because the small amount of air that's trapped inside the shell doesn't have time to ease out through the tiny pores in the shell, like it does when the temperature rises slowly. The air expands at a slower rate and it can escape. That's why you sometimes see little streams of bubbles emitting from gently simmering eggs. When the air expands too quickly, on the other hand, the shells pop from the force.
Boiling eggs also creates that stinky bluish-gray ring around the egg yolk.
When you hard-cook eggs gently, you're much less likely to see, taste, or smell this sulfur.
I learned one method of cooking hard-cooked eggs in the shell at The Institute of Culinary Education (ICE) in New York, but I have long used another method that works just as well.
1. ICE method of hard-cooking eggs: Place cold eggs in a pot with enough cold water to cover them by three inches, plus a splash of vinegar. Turn on the flame, leave the pot uncovered, and the moment it reaches a boil, close the fire. Cover the pot and let the eggs steep for 8 to 12 minutes. When they're done gently shake the pot until the shells crack a little, then transfer the eggs to a bowl of cold water. When cool, shell them.
2. Jill E Duffy method of hard-cooking eggs: Place cold eggs in a pot with enough cold water to cover them. Turn the heat on medium, and cover the pot, but only if you have a clear lid. When the water begins to boil, lower the heat so that the water is just above a simmer, and cook the eggs exactly three minutes—two-and-a-half if you're nervous. Immediately transfer the eggs to an ice bath. When cool, tap them on the counter all over to break the shells, then set them back in the ice water before trying to peel them.