There are about a million articles and Pinterest pins on this. So why am I wasting my time experimenting with this? Well, none of them have ever worked for me. So I did some research and TheKitchn had a nice post about boiling eggs. So I took that and other popular pins and gave it a go. I baked eggs, boiled them starting with cold water, boiled them in hot water and boiled them with baking soda.
I should say that most posts about this subject say that fresh eggs do not peel easily. Eggs have to be aged at least two weeks to properly peel according to most. I had eggs ranging from 6 to 2 days old. I used 6 eggs in each experiment.
This is the first 6 eggs I did starting in cold water, bringing to a hard boil and then turning off the heat and letting them sit for 10 minutes.
I submerged each egg batch in ice water, cracking after a few minutes to let the water seep between the membrane and egg.
This is the baking soda control. I brought it to a boil and then added the baking soda. 
Adding eggs to boiling water (hint: use a spoon to lower them gently in).
Baked eggs. I thought I was clever and put them in my cake pop tray. My cupcake pan is humongous.
The results were clearly in favor of one method for fresh eggs, baked. However, I should have sucked it up and used my huge cupcake pan. Using this pan left a burntish mark on the eggs where they touched the pan. The eggs also had an odd seepage.
I have no idea why they did this.
The yolk was just hard, not yet overcooked. You can certainly tell where they touched the pan. Clearly there is a reason cupcake pans are usually used for this.
What happened with the rest, you may ask. Well peeling was extremely difficult and so…
The pigs loved it!