Arrange the eggs in a single layer at the bottom of a large pot, filling with enough water to reach an inch above them. Cover the pot, bring to a boil, then immediately turn off the heat and keep the eggs in the hot water for a quarter hour. Drain them, chill under a cold tap, then peel and slice in half lengthwise. Scoop the yolks into a bowl and set the whites on a serving tray with the hollow side facing up.