Update: I can't call them "no fail", since I had a bit of an unclean peel on some eggs yesterday, but it was a far cry from what I usually get. It's not a perfect system, it's just a very, very good one!
I'm a long suffering hard boiled egg lover. I never know what kind of result I'm going to get when I hard boil eggs, and I've tried every conceivable method to achieve a clean peeling egg. Sometimes they peel easily, sometimes they don't. Sometimes they crack in the water from bouncing around, other times they don't.
Some people say to use older eggs, others say fresh. Some say to add vinegar to the water, others say salt. I've never found any combination that produces a reliably clean peeling egg. When my eggs are easy to peel, I breathe a sigh of relief, but it's not a result I expect.
I've tried the 'cook them in muffin tins in the oven method', and I found brown patches on the outer surface of the whites where the eggs were in contact with the muffin tin. The eggs were also dry, and clean peeling was not improved over other methods I'd tried. Regardless of what FaceBook tells us about this method, it's not a good one, so don't waste your precious eggs.
No matter the method used, I also found that unsightly gray coating on my egg yolks. Yuck.
As I recently pondered a road trip south, I again thought, "hard boiled eggs would be easy on the road," then I felt the familiar dread. Would they peel cleanly? As I sat and thought about it, something came to me. I wondered if steaming my eggs might work. They wouldn't bounce around in the boiling water, thereby reducing the risk of cracking the shells part way through cooking, and maybe steaming would have some affect on the shell breaking contact with the outer surface of the egg. I decided to try it.
I'm happy to report this method has (so far) worked 100% of the time in yielding a clean peel, regardless of the eggs used (old or fresh). Not only have the eggs peeled cleanly, the yolks have been free of that ugly gray coating I'd come to expect, but didn't like.
As these eggs are not really 'boiled', I call them 'cooked', but that really feels funny to me, so I'm sure I will go back to calling them 'boiled'.
If you, like me, are a long suffering hard boiled egg lover, frustrated with eggs that don't peel cleanly, and yolks that have a gray coating, then I encourage you to try the steam method. Just look at that beautiful egg yolk...no gray coating!
Place 2" of water in the bottom of your vegetable steamer (see note below), and set water to boiling. Add eggs to the steamer basket. When water has reached a boil, set the basket in place, reduce heat to medium, cover and steam your eggs for 20 minutes.
Into a large bowl, add ice and water to create a cooling bath for your eggs. When eggs are done steaming, transfer them to the cooling bath. After 10 minutes, remove the eggs from the cooling bath. Eggs can be used immediately, or refrigerated for later use.
Note: You can also use a lidded pot, with a vegetable steaming basket. These baskets are found on Amazon, or most other online kitchen gadget stores. You can likely find them locally, as well. These baskets are collapsible and generally cost about $10.00. If you use this method, add water to your lidded pot so that it just touches the bottom of the steaming basket.