What I do is a hit the outside of the egg with the back of a spoon until it's all spiderweb cracked.

Then at the bottom (the fat end where the air bubble is) pock the tip of the spoon in and slide it under the membrane the it "spoons" the egg underneath he shell. Then you just twist the egg around the spoon and it seperate a the shell. Once you've done a rotation, lever the spoon away to split the membrane and the shell usually just falls away to a clean egg.

I don't want to say your method is wrong in any way but wanted to piggyback and add my own that I've exclusively used for over a decade.

Steamer basket in a large pot, water up to just below basket. Bring to a rolling boil so it's generating steam. I do this in a steel pot with the lid on and when the lid starts to vibrate and jingle a little I know it's creating steam pressure in there and ready. Then Costco eggs straight from the fridge into the basket, put the lid back on, leave the heat on high to maintain the boil. 12 minutes. As soon as the 12m time is up, straight into an ice bath in a bowl I normally prepare during the last 5 minutes so it has time to chill the water. That's it.

It's seriously been flawless for me every time, hundreds of times. I'm known for bringing deviled eggs to parties and people legit get upset if I don't. Not only is the yolk cooked perfectly but they peel easily with just a single tap on the counter on the smallest tip and then I peel around with my thumb. They look like some Martha Stewart shit, I'm pretty proud.

Hope this helps somebody

I cut the egg in half , then use a spoon to in one pull take the entire half of the egg out of its Shell I always thought every one did the same because it was obvious to me and extremally easy