Ok so what I’m about to say does come with the caveat that I do the pricking a hole in the bottom before cooking and also pouring cold water on immediately after boiling thing so maybe that’s why it works for me but honestly I think this will work even if you don’t. Your problem is that you want to remove the membrane between the shell and the egg, WITH the shell, otherwise it becomes very hard to peel in one go and it takes little chunks of cooked egg white with it at variable depths.
To do that, I smack the top and bottom of the boiled egg on a hard surface to precrack the shell at those two places, then I roll the whole egg very gently on it’s side on that hard surface to create little cracks allover, it’s important not to press too hard especially if it’s softer boiled because it’ll just bisect equatorially with the shell still stuck to both halves in broken fragments. Then, the crucial bit, once you’ve precracked the egg all over, you HAVE to start peeling at the bottom of the egg, that’s the fatter end. There should be an air pocket in there that the precracked shell has sorta of collapsed in to, but hasn’t broken off in shards because it’s all held together by this membrane. If you pinch that loosened cracked eggshell at the bottom between your thumb and index finger to gather and collect it, you can kind of pull it up and off to the side a bit which will cleanly make a tear in the membrane allowing you to just kinda push the rest of the shell off in one piece. Because you can just sorta ease it off, sometimes it likes to come off in a nice big chunk like a jacket, sometimes you need to do a continuous spiral but as long you did that pinch technique you’ll be pulling the membrane off at the same time as the shell attached to it and in so doing you don’t have to pull off little bits of shell by themselves it’s one continuous piece and it can’t take chunks of the actual cooked egg with it like happened in your picture.
I recently came across a horrible piece of software called Silverfast which now doesn’t have a manual anymore. They still have their manuals up to some windows xp version which may or may not still be how certain parts of its operation are done, impossible to know. In lieu of a manual they’ve posted some videos on YouTube, some on Vimeo, different narrators each time, some terrible quality, some just fine, some of them seem from the screen recording to be a couple of versions old, some are more recent. They’re covering single topics so that it SORTA functions like a replacement for the manual in that you can search for topics like one would in a manual and hopefully find a video but it doesn’t function like a manual does since it’s obviously not static and not a proper reference and you’ve got to imprecisely try to seek around to get back to bits where the info you needed was. To add insult to injury, of you search the website for the manual, they have a document referred to as the user manual so you think you’ve finally found it, but it turns out it’s a quick start installer guide which would annoy me at the best of times because normally I’d say the steps are so basic that this document need not exist because it would be impossible to have the level of competence necessary to operate the software without also possessing the necessary competence for basic install but, but astonishingly those instructions are WRONG!
The frustrating thing is that the videos broken up by topic aren’t a bad idea at all, IN ADDITION to a real manual but as a replacement!? I was so pissed.