Heat water to 167°F
Cook eggs for 1 hour
Move eggs to ice water bath for 5 minutes, then peel
This definitely works better with older eggs that have had a chance to lose some water content. (The egg will pull away from the shell more easily, making peeling a lot less of a fight.)
Bring water to a roiling boil
Lower eggs delicately into the water. If you're only doing a couple eggs, you can reduce the heat to a simmer
Cook exactly 7 minutes, then move the eggs into an ice bath
Wait 3 minutes, then peel the eggs