Crack the eggshells all over, all the way around.
Drop them back into the cold water for a short time. This allows water to get under the shell of the egg for easy peeling. We sometimes run the tap and peel them under the running water, this makes peeling even easier.
Peel the eggs and pour away the water.
Then rinse the eggs in a sieve to remove any little bits of remaining shell.
If you can see the yolk of an egg, because of rough peeling, don’t pickle it, just eat it now!