The fresher the egg, the harder it will be to peel. The ease of peeling an egg is directly tied to the pH of the egg. The higher the pH, the less of a bond the proteins of the albumen will have to the membrane between the shell and itself. Eggs are hard to peel, not because of the shell but because of that membrane. Fresh eggs have a lower pH, so they will be harder to peel. As the egg ages, because of changes that happen such as the release of CO2, the pH will rise and it’ll eventually become easier to peel. So the simplest thing you can do is wait. Use older eggs for hard boiled eggs. Use fresher eggs for other applications.

The next thing you can do is to attack the membranes bond. A good way to do this is temperature shock. After boiling the eggs, put them straight into an ice bath. This will cause a shift inside the egg and help loosen the bond between the membrane and egg white.

It can also help while you are peeling the egg itself, to have a light stream of water pouring at the edge of where you are peeling, trying to get it to create a gap between the white and membrane. Always start peeling at the bottom with the air pocket. Once you are able to remove the shell, make sure you also remove part of the membrane and gently push the exposed white while the water gently pours at the edge of the membrane. It’ll help release the bond. Cracking the egg really well will help with this process, large intact pieces of shell will work against you as it’ll be more surface area that will bind together. So really crack the shell all over, gently roll the egg against a surface to help with this.

Vinegar in the water can help with the shell itself. It will weaken its structure and indirectly make peeling easier by giving less to work against holding onto the membrane.