I've been following Julia Child's method to boil eggs since I read it years ago, and it's never let me down. Old eggs, new eggs--they're all easy to peel with this method and the storage method works great. She goes into a 3-page exploration of hard-boiled eggs in her book, From Julia Child's Kitchen, so I know she's done the research. I'm going to highlight the parts I follow that are most important.
Cooking the eggs.
Pierce the large end of each egg with a pricker or pin, going down ¾ inch through the shell. Either put the eggs into a salad basket and lower them into enough boiling water to cover them by at least an inch, or very gently lower them into the pan by twos or threes with a slotted spoon or skimmer. Add 1 ½ teaspoons salt per quart of water, and as soon as water comes back to the boil again, begin timing the eggs, and regulate the heat so that water is very slowly but very definitely at the merest bubble.
Small and Medium – 11 minutes
Large – 12 minutes
Extra Large – 13 minutes
Jumbo – 14 minutes
Immediately after the time is up, drain the eggs, crack each gently by tapping 2 or 3 places very lightly with the back of a spoon, and run cold water into the pan; or transfer eggs to a sinkful of cold water.
Submerge them in a bowl of cold water and refrigerate them.