I prefer to set my eggs on the counter for an hour to get them to room temp. Bring a pot of water to boiling and add vinegar, any kind, I use distilled white because it is cheap. I use about 1/4 cup. Add eggs to boiling water, cover, TURN HEAT OFF, set timer to 12 minutes. (Never boil an egg, you'll ruin it.) At end of 12 minutes, remove eggs to a bowl of ice water to shock them and stop cooking. When cool, dry and place in refrigerator OR peel for immediate use.
To summarize, this method shocks the eggs at both ends of the cooking process. It shocks them by placing them into boiling water to start the cooking process, and shocks them again by placing into ice water to stop the cooking. IMO, starting with cold water makes the eggs tough. Overcooking gives the yolk that grey layer and sulfurous odor. The vinegar loosens the shells, but to be absolutely sure of easy peeling, start with eggs a week or two old. For this reason I date my eggs when I gather them from the nests and reserve the older ones for hard cooking. Again: Never boil an egg, you'll ruin it. Enjoy!