So many egg cooking styles!
I have two methods, both involve room temperature eggs that have slightly runny whites from not being too fresh. When eggs get “aged” like this they have lost some of their water through the porous shell and have a bubble of sulphuric gas starting to build up. This you have likely seen as the fat end of the hard boiled egg having a flat spot on top.
1 sous vide works great. I have a tall Asian noodle strainer like they use in ramen shops, I get my water up to temperature, load the strainer up and put it in the water. This keeps eggs from moving around and bumping into each other and cracking.
2 Bring a pot of water to boiling, lower the eggs in and time for 11 minutes simmering.
Cold tap water run into the pot till it’s cool, I never bother with ice because I don’t have freezer space for it. If you want to crack them right away I agree with the crack and put back in the water for a minute method. Also start at the top of the egg where that bubble lives. I prefer to leave them in the shell and put them back into an egg carton. I think they stay fresh longer in their shell.