Here is a better way to hard-boil eggs and cool and peel them:
To hard boil:
Place the eggs in a roomy saucepan and fill the pan with cold water to completely cover the eggs. Bring to a boil over high heat. Simmer for 30 seconds. Turn the heat off, cover, and let stand for 12 minutes.
To cool:
Leave the eggs in the pan and drain off the hot water. Place the pan, eggs and all, in the sink under running cold water until the water in the pan is cold. Let the eggs cool in the cold water bath for 10 minutes.
To peel:
Drain off the cold water but leave the eggs in the pan. Shake the pan vigorously to crack the eggs. Finish the peel under running water.
Egg rules to live by:
Crack an egg with one good whack on a flat surface to avoid tiny eggshell bits (it takes practice).
Eggs should be stored pointy-end-down in a cold fridge, since at room temperature they lose more quality in one day than in one week fridged.
Egg yolks should not be stored for more than three hours, but egg whites will keep a week fridged.
Room-temperature eggs work better for baking, sauce-making, and pan heating. So, plan ahead.

