Pretty much how I do it now. Better than other ways, but still about every other egg comes out looking as though it’s been gnawed by rats.
Wow - that’s surprising. I’ve almost eliminated my issues this way.
Two or three things - do you roll the eggs on the hard counter? This helps tear the shells away from the whites.
Also - you might experiment with how long you leave them in the ice water. I may have overestimated the time I let them sit. As I think about it, the shorter time would allow the shells and eggs to be more different temperatures and separate more easily. Try one right away and see what happens.
OH - I forgot. I usually peel them under running water, too.
If you want to try a steam cooker, it’s quicker and less messy... I use a “Dash” brand.
Good luck, and Bon Apetit!