Well today's your lucky day, because thanks in part to Rachael Ray and trial and error of my own, I have discovered the ONE TRUE WAY to cook a perfect hardboiled egg.
First - Put your eggs in a pot.
Second - BARELY cover with room-temp water.
Third - Place the pot over high heat (do not cover).
Fourth - Bring to a boil.
Fifth - BOIL ONE MINUTE. No more, no less.
Sixth - Kill the heat and COVER.
Seventh - Let sit for TEN MINUTES. No more, no less.
Eighth, and this is where it gets really exciting - Drain the hot water and shake your eggs around in the pot to get them all smashed up. This step is important, I promise.
Ninth - Cover eggs with frigid water.
Tenth - Allow to sit for FIVE MINUTES, replacing the water as it warms up.
Eleventh - Peel.
The importance of breaking the shells before cooling is this: The water gets in there and makes them easier to peel! So following these instructions will not only result in a perfectly cooked egg with no green:
It will also allow you, too, to do this with the shell:
Therefore, I firmly believe that the ease of peeling has more to do with cooking method than freshness of the egg. DO NOT CONTRADICT ME.