This is what I do and it always works.
Gather your eggs (or use what you have on hand). Bring a pan of water to a boil, lower the eggs gently into the boiling water. When it resumes boiling, cover it. You can reduce the heat to simmer or you can turn it off. For large or extra large hard boiled eggs I let them sit 15 min. If you have smaller eggs or want soft boiled the time will be less.
Immediately, drain that water, run cool water over them then dump them into sink or bowl of ice water. It is okay to crack the shells then but I don't find it necessary. When they are chilled in 5 minutes or so, crack and peel starting at the large end.
I used to add 1 tsp salt, some people add vinegar, etc. but this is simple and it works. The key is put the egg in boiling water, reduce heat, do not over cook., cool immediately. This also eliminates the greenish color on the yolk.
I have boiled 100 + this way with the addition of 1 tsp salt and they peeled perfectly 95% of the time regardless of age. Lately I have not been adding salt and so far they are peeling perfectly at the same rate.
I would love to hear how this works for you. Bon Apetite