I add white vinegar to the water, a couple tablespoons is all. It changes the acidity of the water, helps separate the egg from the inner membrane.
I lower the eggs into boiling water with tongs or a spoon. To reduce cracking, I set them on top of an egg already in there, helps reduce the shock as they don't fall to the bottom of the pan to crack. let them go for a while. I have a timer, maybe I should use it.
When I think they have had enough, they go into the sink. Pour off the hot water, keep them under the tap to cool. When cool enough to handle I tap and roll them gently to crack the shell completely. They go back into the cool running water for a while. With the cracks, the water is able to penetrate the shell and in places, the inner membrane. I never, ever peel them when hot. Warm eggs are considerably more tender than cool eggs. I peel them underwater, letting the water act as a lubricant. I get the peel started from the big end and often the shell rolls right off. I get some here and there that come out looking like the moon, but most of the time I end up with a smooth egg.
Temperature shock going into boiling water and cooling down as fast as you can seems to have the greatest effect.
You need strong shells in your eggs. Weak shells don't seem to peel as easily. Make sure your birds are getting enough calcium. I save my shells, dry them in a bowl in the sun, crush them up and toss them in to the pen. The birds gobble it up, gives them something for the gizzard and a source of calcium.
