As grandma taught me, when your eggs are cooked, they should be plunged into ice water, this shrinks the membrane around the egg and separates it from the shell, the other thing is -one the eggs are cool, and that should be soon, cause if your ice water gets warm you need to put more ice in(immediately)- tap the shell all over on a counter top to 'spider web fracture' it - like an auto window, any place that was not cracked will stick! I roll it around to make sure the outer shell is all mush but not the egg inside, you can then peel the whole thing off, sometimes in one piece.
I've never put salt in the water, vinegar, may keep the shell from cracking, but not always, so why waste, I add nothing.
That green line around the yoke? Thats from over cooking the egg,
I always use fresh eggs, they always taste better, the whole trick is the ice water and fracturing the shell all the way around, been doing that since I was a little kid, and you want them really really cold, and it always works. Happy shelling!
Ps you dont have to peel them right away either, they keep better in the shell in the fridge without absorbing any other taste.
x2!!
Put the eggs in a pan, cover with at least an inch of water, put it on the stove, bring it to a boil. Let them boil 1 minute, remove from heat, cover and let sit for 17 minutes. (this amount of time ensures they're done, no matter what size egg, amount of eggs, shape of pan, etc...and won't over cook them) Pour off the hot water, start running cold water over them, pour the cold off a couple times, leave a little in the pan, and dump ice over them, gently so you don't bust the shells, unless of course you don't care... Let them soak in the ice bath till they cool, and either peel them right away, or put them in the fridge. When you peel them, roll them around on the counter too crack all of the shell. If they start to stick at all, peel them under cold running water.
Works like a charm for me, and I LLOOOOVVVVEEE hard boiled eggs, and egg salad! (So I boil a lot of fresh eggs!)
Vinegar in the water keeps the whites from oozing out if they crack in the pan. Never use it, or salt in the water. (I mean I've never used it...you can if you want too, of course!)