How to completely peel a soft boiled egg without destroying it?
Cool the egg in cold water, crack both ends of the egg by tapping the egg, and the shell will peel off easy.
I usually stick the pot under the faucet after letting the water run for a few minutes to warm up. Then have it run until the water is no longer steaming hot. I take an egg out and, using a sterile surface, I'll turn the egg while cracking the middle.
Don't bother trying to peel the egg - it takes a long time and the egg will be torn up. Just take a teaspoon and tape around the center of the egg to split the egg in half. Then spoon out the egg into your dish. The egg will slide right out.
After that I crack it twice on top and twice on the bottom. Don't use too much force or the egg itself will crack. Typically it will slide right off. Make sure you're feeling it under the water because it helps to separate the membrane from the egg.
If the membrane doesn't break when you start peeling the shell off then it's going to stick. You need to break the membrane, which I can usually do with my fingernails.
Another old trick is to add a ps a white vinegar to the water once it starts to boil. The vinegar helps remove the shells after cooking, and if the shell cracks while boiling, it'll help keep the egg from bursting out into the water.