It never occurred to me that I still had something left to learn about peeling boiled eggs.

However, the other day when I was running some oeufs mollets—boiled eggs with firm whites and gooey yolks—under cold water to make them tolerable to peel, I dropped one onto the bottom of the pan.

The shell splintered, so rather than taking it out of the water and rolling it around to break up and loosen the shell, I did it in the water. To my surprise, the fragile egg became much easier to peel. The water got under the shell and seemingly liberated it and the thin membrane underneath. After that I had an absolute orgy of egg boiling and peeling.

Reference: How to hard boil an egg (Cookthink)
Reference: What's the difference between white and brown eggs (Cookthink)