A friend told me she bakes the whole egg in a muffin tin and they peel the easiest she's ever tried. I haven't done it yet--still using the boiling water and quick cool method.

Try shaking egg(s) in small covered container that has some water in it.

I peel the boiled eggs under water, so much easier!

Thanks for the suggestions. I'll try watching the age of the eggs and maybe peeling them when they're still warm. Hopefully better results :-)

Buy an egg cooker. I have one that a friend bought me for my birthday about 4 years ago. I have never had an egg stick again. It will boil 7 at a time and no matter how fresh or not they are, they never stick.

Farm fresh eggs have larger yolks and sometimes not enough white to stay intact when you use them as devilled eggs. Or at least that has been my experience. Somewhere DH heard to take the hot eggs put them in a tuperware like container and put them in the fridge to cool. They sweat making the shells easier to come off. Or at least that's the theory. Works for him. Whenever he finds out a trick to use in the kitchen, that becomes his job. Sp far he's the dish washer loader and the grocery putter upper.

I have used the same method to boil, set timer for 25 minutes, drain off hot water. THEN with lid ON, SHAKE the eggs to crack the shells, fill pan with cold water and then peel.
I have the Instant Pot pressure cooker now, put in 1 cup water and layer eggs on bottom rack in silicone baking cups, to fill pot, cook for about 5 minutes. I peel while rather hot so I can pickle them and have them seal to store in the spare fridge.

Cuisinart Egg Central. I love this thing. Oh how I hated boiling eggs and peeling before. I had my method, but this is so much better hands down. Wish they had been available 50 years ago!

I put a little oil in the water, when done boiling cool quickly with cold water Shell will come off easily.

I think the cooling quickly is very important. If eggs cook too long or are not cooled quickly, the yolks turn dark around the outside. I don't think it really hurts the egg, it's just unsightly.

The trick I have tried lately for potato salad or egg salad is to poach the eggs. I can put up to seven eggs in a flat pan with a few inches of boiling water. When eggs are cooked, pour everything into a strainer. Then you have yolks that are a little oval shaped instead of round, but that's a "design choice".