Hard-boiled eggs should be at least 4 or 5 days old; too fresh (a rare circumstance), they are impossible to peel. It is said that they must be room temperature before being put to cook, but, inasmuch as they form a part very often of last-minute-decision preparations, this rule cannot always be respected and I doubt that the dish is the worse for it. Many claim that the only correct way to hard-boil an egg is to lower it into rapidly boiling water and cook it for exactly 9 minutes. I prefer to begin the eggs in cold water, bringing it to a boil over medium heat and leaving it just under a simmer for 10 to 12 minutes, depending on the size of the eggs, their number, the quantity of water, etc. (The quantity of water and the number of eggs affect the length of time necessary for the water to come to a boil, and the longer it takes to come to a boil the less time the eggs should remain at the boiling point.) It seems to me that, done this way, there is less danger of the shell’s cracking (particularly should the egg be refrigerated) and that the white remains tenderer. Whatever your method, the important thing is to avoid overcooking, which dries and dulls the flavor of the yolk, coating it at the same time a disgraceful blackish green, and turns the white to rubber. If, through misjudging the time, the very heart of the yolk should remain slightly liquid, that is no problem—it is at least as good that way.