I have found a method for hard cooking very fresh farm eggs that has worked perfectly every time.
I imagine the method would work for store bought eggs too.
I usually cook about six eggs at a time.
Heavy pot. Gently put in the eggs. Add enough cold tap water to cover the eggs by about an inch. Bring the water to the boil slowly so the interior of the eggs can cook at the same rate as the whites. Gently boil the eggs for about four minutes.
Drain the hot water. Run cold tap water to fill the pot. This next bit is very important IMO. Put one of those frozen freezer packs in the pot or a couple of trays of ice cubes. Let the eggs completely cool for at least half an hour.
Peel the eggs. Works everytime.