I have tried just about every single way of trying to get my farm fresh eggs perfectly boiled with a shell that peels off nicely. Anyone that keeps chickens knows that peeling a very fresh egg usually ends up with a lot more egg attached to the shell than to the egg itself. I've tried baking soda, salt, and vinegar in the boiling water. I've tried boiling for a certain amount of time and then cooling quickly. I've tried shaking the pan to crack the eggs a bit. I've had limited luck with all of them.
Then, one day I was cruising down the internet rabbit hole and came across a very simple recipe for steaming, instead of boiling, eggs. I was intrigued. The recipe was short and simple and it promised eggs that peeled easily. I sure wish I could backtrack and remember which website I found this on because I would love to give them credit!
Here's the recipe:
Fill steamer water to low level. Put eggs in steamer.
Set steamer for 20 minutes.
Put the hot eggs in an ice water bath as soon as the timer "dings".
Keep eggs in ice water bath until cooled.
I've found that about 95% of the time the eggs peel completely clean. The eggs are perfectly cooked without the sulfury green ring and the texture of the whites is cooked without being rubbery. You can see that the yolk of the this egg is very slightly undercooked in the center. I think they didn't cook quite as completely because I put so many eggs in the steamer. Usually I would cook 4 - 6 eggs at a time. But the taste is not affected at all!
Let me know how steaming your "hard boiled" eggs works for you!