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I also steam my eggs in a steamer basket for 12-15minutes then place in cold water before peeling. There is never a problem getting the shell off and eggs are prefect every time.

The old-timers of New England, New Hampshire to be exact, said to leave the eggs out at room temperature for a week with the pointed end up, then boil and peel with ease.

I heat about an inch of water in a 2 qt pan, bring to a boil, and insert a steamer basket and 6 large eggs. Cover, steam for 12 minutes and immediately place eggs in ice water for 30 minutes.

Add me to 'Team Steam' when it comes to eggs. I'm a perfectionist who HATES to see a hb egg with that awful green ring around the yolk. I use a vegetable steamer in a pan of water. Bring the water to boil, add the eggs, cover and simmer for 12-14 minutes for perfectly hb eggs. (lean toward the lower end if you want eggs for potato salad, the higher end if you want them for eating out of hand)

I put water in my pan and add eggs to cover with 3" of water. I add one teaspoon salt and 2 tablespoons of vinegar to the water. I bring the water to a boil and turn the heat down so that the water just maintains a soft boil. I boil the eggs for 10 minutes and then pour off the hot water and add cold water. I drain and rinse the eggs twice to dissipate the heat, and then I let them sit for five minutes to cool off. By this time they are cool enough to peel. The vinegar helps the eggs to come out of the shell easier when I peel them. I usually boil a dozen at a time, but you can boil less eggs. I make egg salad with my eggs or put them in to the refrigerator after peeling to have for a quick breakfast the next day. The eggs in the store are about three weeks old when we buy them, so if they are very fresh they might stick to the shell. If you are using fresh eggs and want to boil them, let them sit in the refrigerator for a few weeks. My eggs are collected fresh everyday so I know how old they are.

To peel eggs easily, add a little baking soda to the last few minutes of boiling, egg shells will peel off easily.

I use my Ninja air fryer. Place about half dozen eggs on the rack. Use air fry selection at 250 degrees for about 20 minutes. Time may vary on size of eggs. I use large eggs. Once eggs are done place in a cold water bath for about 10 minutes. No watching the stove. Eggs peel nicely.

I used to do it that way but sometimes the eggs weren't quite done enough. Now, I bring them to a full boil and boil them for 20 minutes.
To make them easy to peel, I plunge them in ice and water.
Note: Older eggs are so much easier to peel. Try buying a dozen and keeping them for about two weeks before cooking.
Good luck!

I cook mine the same way you described but I call them hard cooked eggs in the shell. Some cooks boil excessively but the heat could destroy the protein in the egg whites.