I have learned that you never "boil" eggs. You cook them. Bring the water just to a boil, then let them simmer. If you have farm fresh eggs, let them sit on the counter at least over night. No, you won't die from eating an egg that was sitting on the counter overnight. Most people in other countries do not refrigerate their eggs. They just turn them over each day or so.
The cold water cooling is good, as is cracking the eggs under water. But cool them soon and fast. Right after the cooking time is done.
Happy cracking.