This method works on a simple premise: If you don't boil the bejesus out of your eggs, they won't turn green, foul-smelling, and hard as nonlethal bullets. Instead, let them relax in a nice hot bath, gently firming up in even heat, and they'll be tender with bright, smooth yolks.
Put the eggs in a pot. (If you have to stack them to fit, use a bigger pot.) Add enough cold water to cover the eggs by an inch. Set over high heat.
When the water's at a full boil, turn off the heat and cover. Let the eggs sit for 9 minutes (7 if you like an almost spreadable yolk). Fill a bowl with ice water.
Transfer the eggs to the ice water to stop the cooking. ("Shocking" them like this makes them easier to peel, too.)
To really make hard-boiled eggs special, marinate them after cooking. Make a classic Chinese dip by adding a stick of cinnamon and some black peppercorns to 1/2 cup of soy sauce, 1 cup of water, and 1 tbsp of sugar. Simmer for 10 minutes. Let cool. When the eggs are done cooking, peel them and set them in the dip for an hour or so. To get a marbled look (like the egg on the left), rap unpeeled eggs on the counter to put some big cracks in their shells, then drop them in the marinade for 2 hours or more before peeling.