Let me put some context to this question.
Sometime ago I checked into this hotel (it no longer exists). It used to be some mansion, and a chain converted it to a routine hotel. Lousy sound insulation, but I'm digressing.
The breakfast was included, and said breakfast consisted, among other things, of a huge bowl filled with boiled and peeled eggs.
I didn't pay much attention to it at the time, but looking back at it now, I marvel that anyone can boil and peel a huge number of eggs and get everyone of them this perfectly peeled. My own talent, which includes pouring a generous amount of salt in the boiling water and plunging the eggs into cold water promptly 3-5 minutes after boiling, produces the rather unapetizing result you see below.
This answer seems to suggest that freshness is incompatible with ease of peeling. I hope that hotel, and workers, didn't merely rely on archeologic eggs to obtain this perfect peeling. I don't recall an unusual taste.
How can I obtain nicely peeled boiled eggs, every time?
To make the question a wee-bit harder, I'm often aiming for a soft core, removing from the heat about 2-3 minutes after the start of boiling.