Place your eggs in a pan and cover by at least an inch or so with cold water. Turn the flame up high and as soon as the water comes to rapid boil. Cover the pan and turn off the flame. Allow the eggs to sit covered for 12 minutes. Transfer eggs to a bowl of ice water. Peel and eat when ready.
I have found that this method cooks the egg without turning the yolk chalky or green. The ice bath afterwards creates better separation between egg and shell, making it easier to peel.
I've been boiling my eggs like this for years, however, as soon as they boil I continue at a low boil for a minute then cover the pan and turn off the flame etc. etc. (what Kirk said). Also, I just pour off the water, add ice and water in the pan (instead of the transfer to a bowl). When boiled eggs are done and ready to peel it's easiest if you crack and shell them under running water...they slide right off.
I've tried this on an electric stove and it didn't work well. Not sure what went wrong. Maybe someone has input for electric ranges.
This really works...
I find the best way to "De-Shell" hard boiled eggs is...when their done run some tap water into the pot with the eggs(to cool them down a bit) and then leave a little bit of water (so the eggs can slide around in the pot) and then shake the pot and let the eggs hit the sides of the pot and each other and they will break up the shells pretty good(sometimes peeling the whole egg while shake'g) without breaking the eggs. Then take the egg in hand and under running water peel away whats left...the shells should come off pretty ez and somethimes all at once and it should leave you a hard boiled in tack and in hand...ready for the next step....EATING! Good Luck. Cheers.