Every Easter, we would make a dozen eggs for each of my children, and there were four children. I got tired of pulling hard boiled eggs out with cracked shells. Over the years, I learned more, and more about the properties of eggs, at what temperatures the egg whites set, what temperature the egg yolk sets, how long it takes to hard boil an egg using various techniques.
The link Andy provides gives you eggs that are easy to shell. But sometimes you end up with cracked shells. If you want uncracked shells, and want to prepare a dozen, or more eggs at a time, this is the method that works for me.
First, let me explain that you don't need boiling water to cook a perfect hard boiled egg. Water doesn't boil until around 212' F. The eggs begin to set at about 160' F, far lower than the boiling point of water.
Boiling water is turbulent, and jostles the eggs around, which can cause them to bump against each other, or the side of the pan. This can crack the shells. Here;s how I hard boiled as many pans as would reasonably fit in my largest boiling pot (dutch oven).
Place eggs gently into pot, filling to 2/3'ds full (24 eggs in my pot). Fill pot with cold water to cover by 2 inches. Cover with a glass lid. Place pot over medium-high heat and bring to a very light simmer bubbles just startling from the bottom). Reduce heat to medium-low, and cook for 5 minutes. Turn off stove and let the eggs sit in covered pot for 5 more minutes. Place pan into sink, remove lid, and turn on cold water, letting it slowly replace the hot water until the pan water is all cold. Carefully remove the eggs with a silicone spatula to baking sheet lined with paper towels to dry.
If you plan to eat the eggs immediately and hot, use And's method. If you are making hard boiled eggs for deviled eggs, use Andy's method. If you are making hard boiled eggs to be eaten cold, or to be colored as Easter eggs, use my method.
Either technique will give perfectly cooked, hard boiled eggs.
Egos cooked to too high a temperature will cause the egg whites to become rubbery, and if way overcooked, to change color next to the yolk. Also, the yolk will become dry instead of creamy. When cooked just right, the yolks are fully set, but still give you a creamy mouth feel.
If you ever have a hankering for soft-boiled eggs, this makes them perfect on my stove, with fully set whites, and fully soft, but ot yolks.
Place one to three eggs in a sauce pan. Add cold water to cover the eggs by 2 inches. Add 1 tbs, salt to the water. Turn heat to medium high. Bring the water t a light boil. When it just begins to boil, set a timer for 2 minutes, 32 seconds. Turn down heat to simmer.
When the timer goes off, immediately remove the pot from the heat and pour off the not water. Bounce the eggs around in the pan to crack them all over, and fill with cold water. Under running, cold water, gently peel the eggs.Serve on buttered toast, or toasted English muffins.
Seeeeya; Chief Longwind of the North
I am intrigued by the steaming update, though, GG. I just might make a half dozen eggs later today. I wonder if deviled eggs go with ham fried rice... 
