I am happy to report that after a year of trying everything under the sun, I finally found a fool proof method that works. So I have to share it...and just in time for Easter!
I put my eggs in a pan with cold water and 1 tsp of baking soda, making sure to cover the eggs so that there is at least an inch or two of water above the top of the eggs.
Next, put the pan on the stove on high heat. When the water comes to a good boil, put a lid on the pan and remove the pan from the heat. Let it sit for 15 minutes. When the 15 minutes is almost up, fill a bowl with ice and water. After the 15 minutes, use a slotted spoon and remove the hot eggs from the hot pot and gently put into the ice water. Repeat this with each egg. Once all eggs are in the ice water, let them sit for 15 minutes.
At the end of the 15 minutes, you can either peel the eggs immediately (they will keep for up to one week peeled in the fridge) or put them into a bowl in the fridge till you're ready to use them. I usually do the latter.
When I am ready to use the eggs, I tap each end of the egg on the counter top. Then under cool water, I roll the egg between my hands, and starting at the wider end, I begin peeling the eggs. Doing it under cold running water helps. I start at the wide end, because that's where the air bubble is and it seems to make peeling easier. My friend, Lauren, sent me this video about egg peeling. The cooking is pretty self explanatory, so if you play it you may want to skip ahead to the end where it shows how to peel the eggs. It uses a different method than mine, but it sounds like it would work great.
I can't tell you what a boon this is for me to finally be able to cook and then peel a hard boiled egg with ease. It makes my life a lot easier. And the eggs come out cooked perfectly...completely yellow on the inside and no green rings around the yolk. Love it! Who knew that perfect timing and 1 tsp of baking soda would be the ultimate answer? Happy Easter eggs everybody!