Here's the way I've been doing it for years, and it really works well for me.

Bring the eggs to room temperature. Start the water boiling and plop the eggs into the boiling water (you can't do this with cold eggs or the shells will break). Boil for 15 minutes, then use a slotted spoon to transfer the eggs to a bowl of ice water.

The shells just seem to fall off when I do it this way.

Good luck.

Jeannie