Easy-to-Peel Hard Boiled Eggs.

How to Make Perfect, Easy-to-Peel Hard Boiled Eggs > Willow Bird Baking:
When the water boils, immediately cover the pan and turn off the heat (leaving the pan where it is).
Let the pan sit for 5 minutes.
Transfer the eggs to a separate bowl to cool for 2 minutes.
Run cold water over the eggs for a few seconds after they’ve cooled and then drain it off.

Peeling eggs so much easier:
Instead of bringing eggs up to a boil from cold water, drop eggs directly into boiling water.
After removing them from the hot water, plunge them into an ice bath immediately and let them cool for at least 15 minutes.
Never let finicky shells deter you again.

From Serious Eats' J. Kenji Lopez-Alt: The Food Lab: The Hard Truth About Boiled Eggs | Serious Eats
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