Carefully add the eggs, then turn the heat down to low and simmer for 12 minutes. You want bubbles, but not be a rolling boil.
While the eggs are cooking, prepare an ice bath. Fill a large bowl about halfway with ice, then add water.
Transfer the cooked eggs to the ice bath using a spoon or a mesh strainer. Let cool in the ice bath for 10-15 minutes. At this point, you can transfer to a bowl and store the eggs in the refrigerator for up to a week.
Store cooked and peeled eggs in a sealed container in the refrigerator for up to 3 days. Unpeeled eggs can be stored in a bowl or in their original carton for up to a week.