The best tip on how to properly hard-boil, without getting grayed yolks, is to put the eggs in enough water to cover well ("covered by 2 inches", but as long as they're covered, they're good, IME). Bring the water to a boil, and turn it off. When you can comfortably rescue the eggs from the water (below 140 deg F), they're done, and not overdone.
Now, how to get them to peel easily. Serious cooking guides (that actually test their own advice) seem to agree the most important factor is using old eggs. Fresh eggs won't peel well. Eggs that are at least three days old peel well. Here's one instance where your grocery store's high turnaround can work against you. Fortunately, they intentionally cycle the oldest perishables to the front, so the ones you pick up are likely to be the oldest available.
Another tip that supposedly works is to plunge them into ice water, after cooking. Tonight, I boiled 3 dozen eggs, and tested this theory. One dozen went straight from hot water to ice water. 10 of them peeled well. Another dozen sat in the slowly cooling hot water (now just warm), and I peeled them next. 8 of them peeled well.
OK, 10/12 versus 8/12. Probably significant, but not overwhelming. But wait...
I took those 4 eggs from the warm water, and soaked them in ice water. Three of those became really easy to peel. Ta-dah! Ice water saved hard-to-peel eggs!
Clearly, it's not important that the eggs get plunged immediately from the hot water into the ice water. My feeling is, after peeling 36 tonight, that the ice bath firms up the whites, making it easier to pull the sticky shell membrane away. As long as the egg is chilled, the outer flesh is firm, and it works. Cooling them slowly, and refrigerating them before peeling, should work just as well. But that test is for another day.
So, to summarize, here's how to make great hard-boiled eggs:
- Buy eggs a few days ahead of time if possible, because older eggs peel better.
- Cover the eggs with plenty of water, bring to a boil, then cut the heat.
- When the water cools to a touchable temperature, fill a bowl with ice water, and spoon the eggs into the bath. Once chilled, they will peel easier.