Thanks to food scientist Shirley Corriher and her book Cookwise, there’s a ridiculously simple method that produces sunny yellow yolks (with no blue-green discoloration) and whites as tender as a baby’s bottom. Over the years I’ve simplified it even further.
Cover the eggs with 1 inch of cold water in a saucepan (Corriher uses 1½ inches, but 1 inch works well for me). And don’t just eyeball the measurement; use a ruler. Also, make sure the lid’s close by.
Bring the water just to a full boil, then remove the pan from the heat, and cover it with the lid. Let the eggs stand 10 minutes (if you want a slightly moist center to your yolk), or 15 minutes (if you want a fully-cooked yolk).
Pour off the hot water, then fill the pan with cold water and add some ice cubes to cool down the eggs quickly. Let them stand in the ice water 5 minutes, then drain.
Peeling: If you aren’t dyeing the eggs, and you’re consuming them soon, I’ve found they’re easier to peel if you crack the egg shells gently all over while they’re cooling off in the water, then peel them while they’re still submerged. If you’re holding onto them for a while, peel under running cold water.
When talking eggs, the freshest are always best, except for hard-boiled; older eggs are easier to peel. Aim for 1 to 2 week old eggs. To tell how old an egg is, watch how it behaves in its shell in a pan of cold water:
Stays on its side on the bottom: 3 to 6 days old
Stays on bottom with wider end tilted up slightly: a bit more than 1 week old.