I use a steam cooker now, but this will work with a pot of water as well:
As soon as they are done (still very hot), VERY QUICKLY put all of them in ice water. Prepare a pot of ice water early, with ice cubes having time to get the water cold. Have it ready - no delay.
After a few minutes (2 or 3 does it for me) - take the eggs straight out of the ice water and tap them on the side by putting them firmly on a hard surface, cracking the shell. ROLL the egg under your hand on the clean, hard surface, fracturing a large part of the shell. Squeeze a bit in your hand, and begin to peel. I find it often comes off in two or three big pieces.
I like pickled eggs and use your method. It is amazing how much shell comes off in slabs! Easy way to peel lots of eggs for pickling.