Cooking Japanese ramen eggs, shell sticks to membrane

The author makes hard-boiled eggs using a specific method, involving boiling water, salt, and eggs directly from the fridge. Eggs are punctured before boiling for seven and a half minutes and then placed in an ice bath. While the eggs are cooked perfectly, the author consistently struggles with peeling the shells. Some shells peel easily, but others are stubbornly stuck to the egg, often causing the egg white to tear off. They try using a teaspoon to separate the shell, sometimes succeeding but often damaging the egg. This peeling inconsistency occurs even with eggs from the same carton. The author wonders if the boiling temperature wasn't high enough or if the ice bath wasn't cold enough. They note the ice bath remains cold even after an extended period. The author is seeking to understand why some eggs peel perfectly while others are ruined during the peeling process.