
Traditional kitchen advice says you must dunk hard-boiled eggs in an ice bath to halt the cooking and make peeling easier. But only part of that is true, and the other part can easily be bypassed—meaning you can skip the ice altogether.
Plunging eggs into ice water doesn’t improve how easily they peel. I know this firsthand from recently cooking countless hard-boiled eggs—none of which required an ice bath. The key to easy peeling is starting the eggs in hot water, not cold. Starting them in cold water and then boiling bonds the eggs to the membrane, making them tough to peel. (Pressure-cooked eggs, however, peel effortlessly.)
If you're just cooling a few eggs, placing them in a bowl of cold water will do the trick to make them cool enough to handle. Once they're no longer scalding hot, you can peel them with ease, leaving the white intact.
While ice water doesn’t help with peeling your eggs, it does stop the cooking process. However, eggs are more forgiving than delicate vegetables like asparagus, which really benefit from a good shock. To avoid overcooking, simply reduce your cooking time to begin with.

The three eggs shown above were all cooked for five minutes under high pressure in an Instant Pot, followed by a manual release. The egg on the left was rinsed under cold water until it cooled enough to peel immediately, while the two eggs on the right went into a bowl of cold tap water with four others. As seen, the yolks on the right are a bit firmer and paler, but there's no unpleasant gray ring of sulfur. If you want to avoid even that slight extra cooking, simply reduce your cooking time by a minute and use the residual heat to finish the eggs.
If you prefer using an ice bath, feel free to keep doing so. Just don’t expect it to make peeling any easier, and don’t worry if you ever find yourself out of ice. You can still cook eggs perfectly and peel them with ease, even without the ice.