Here's how to make perfect, and easy peeling, boiled eggs. Carefully (so you don't crack them) place eggs into already boiling water. Boil for twelve minutes. Drain and immediately place eggs into bowl of ice water (lots of ice). Let sit twelve minutes. Eggs peel easy. The drastic and sudden change in temperature has caused the membrane to separate from the egg.

Alternatively, you can skip the cold water if you use a wet teaspoon to remove the egg from its shell. It's easy. First, after cooling eggs in cold water to the point you can handle them, crack a line around the egg's equator with the spoon. Then slip in the wet spoon under the shell and remove the shell from one hemisphere, re-wetting as needed. Then do the same for the other hemisphere.