I've tried many methods and this has consistently yielded the result I prefer for my egg salad.
My perfect hard boiled eggs this morning. Best method of all I've tried. Aren't they gorgeous? These are pasture raised eggs from Aldi.
While you're boiling water, prick the round end of an egg with an ice pick or something pointy, just a little bit to get into the air chamber of that larger end of the egg - not too forcefully or you'll break the egg. This hole will prevent the egg from cracking.
When the water returns to a boil, lower the heat to a gentle boil.
When the 13 minutes are nearly up prepare an ice bath and remove the eggs with a slotted spoon and put them into the bath.
Let them cool sufficiently, remove them, tap and roll them. Peel them under running cold water.