Perpetually Perfect and Peelable
Firstly, it's MOST important that after the hard-boiled eggs have finished boiling, that they be immediately rinsed in and then left to soak in very, VERY cold water -- the colder the better, icy is best. This insures that the shell will separate from the albumen (the thin film that separates the shell from the egg) allowing us to peel the egg.
THEN, I find that the best way to peel a hard-boiled egg is to tap both ends on a hard surface, breaking the shell on both ends and then laying the egg on its side on the hard surface, simply and quickly rolling it gently but firmly against the hard surface which causes many, many tiny and larger cracks to form through the shell and then it's ready for easy peeling.
As an added extra... I find the wisest way to hard-boil eggs is to put all the raw whole eggs (as many eggs as you like as the number of eggs you will be boiling has nothing to do with this cooking method) into a pot that has a tightly, snugly fitting cover of its own -- then cover all the eggs, filling the pot, with cool or lukewarm tap water until there is more than one-inch of water covering the egg that is on top of all the eggs in the pot. Then, on a high-flame, bring the water to a full, rolling boil... the very minute the eggs reach that full, rolling boil, remove the pot from the stovetop to a nearby waiting trivet and IMMEDIATELY put the cover on the pot completely covering the pot TIGHTLY and allow the eggs to continue to cook in the hot water (right on your tabletop, yes, without any flame underneath it) still in the pot for EIGHTEEN minutes. After the 18 minutes, remove the cover and bring the pot to your kitchen sink, gently and carefully pour out the still very very hot water and refill the pot with the coldest water you can get your tap to produce. Let the eggs just sit in the very cold water for a minute or two and then refill the pot again with more of the coldest water you've got. And you will have perfectly hard boiled eggs (which will also be remarkably easy to peel -- THAT is the secret to easy egg-peeling, immediately rinsing the cooked eggs with the very coldest water you can). I got this egg-boiling method from the old Betty Crocker cookbook and I was happily amazed to realize that it really works -- PERFECT hard-boiled eggs EVERY single time -- and NEVER any soft uncooked spots inside the eggs either. It's just great.
Miss Freya Friedman