I used to have to boil and peel a LOT of eggs every day, so it was critical that they were cooked correctly, and that they peeled easily.
To keep the eggs from cracking in boiling water, allow them to warm up to room temperature first. Takes about 1/2 hour or so. Don’t worry, eggs don’t go bad as fast as everyone thinks. They can safely be left unrefrigerated for many hours.
I used 2 pots.
Put a pot of water on to boil.
Put the (room temperature) eggs in another pot, and set it aside.
When the water boils, replace it on the heating element with the pot of eggs, and pour the boiling water over them. Set the empty pot in the drainer (It’s clean already, and it so hot that it will be dry in a minute).
Don’t let them boil for more than 10 minutes, or they will be overdone, and hard to peel.
Then, just as Sycorax said, run cold water over them immediately and they will peel much easier. When I had access to such luxuries, I even put a large scoop of ice in the pan.
Roll the eggs on a flat surface to create a belt-like cracked region all around the egg, and the two halves of the shell will twist right off. Rinse the peeled egg under cold water, set it aside, and grab another one.
You can peel about 12 eggs per minute this way.
“Oxen are slow, but the earth is patient.” – some Chinese guy