Place the eggs in a large saucepan. Fill the pot with water until it covers the eggs by one inch. Cover the saucepan and bring to a boil over high heat. Once at a rolling boil, turn the heat to the lowest setting and let the eggs simmer, covered, for 10 minutes. Turn off the heat, remove from the burner, and let sit, covered, for an additional 5 minutes on a cold burner. Pour out the hot water, rinse the eggs by running cold water over them a couple of times, then add ice cubes or ice packs. Let stand for another 5-10 minutes in the sink until the ice is melted and the eggs are cool.