Martha Stewart's method, and er, stuff.
I glanced at Martha Stewart's method in a local newspaper, and immediately dismissed the cooking time as a typo. For years now, I have been boiling eggs by putting them in a pan with about an inch of water to cover, bringing the water to a full boil, turning off the heat, letting them cook for twenty minutes, then plunging them into ice water. They always come out perfectly cooked.
However, I hadn't noticed the part in her method about lidding the pan, or perhaps the paper left it out. I suppose this would account for the difference in time, and I'll have to try it this way.
As was said, there is really no wrong way to do it, but I prefer starting the eggs in cold water for one reason: It eliminates the possible variation in water temperature. One person's simmer might be 175 degrees, another's might be 200, and this can make quite a difference in how much the eggs get cooked over the total time. Also, putting a lot of refrigerator-temperature eggs into a pot of simmering water can significantly lower the temperature of that water, resulting in undercooked eggs. Three are not a big deal, but a dozen, on the other hand...
I'm not saying you can't get good results with this method, obviously you can. I just think it introduces a variable that isn't there with the method I use. As to the need to watch the pot until it boils, I just attach my probe to the side of the pan, and set the digital thermometer to sound an alarm when the water reaches a boil.
Speaking of peeling eggs, I know of three things that are supposed to make the eggs easier to peel. The first is using older eggs. The second is plunging them into ice water, which as well as stopping the cooking, is supposed to loosen the bond between the egg, the membrane, and the shell. The third is to put baking soda in the water (for no good reason I can think of)
However, it has been my experience that no matter what precaution I take, there are always at least one or two in the batch that just don't want to be peeled. Does anyone have a sure-fire method they would care to share?