Cook for 10 to 15 minutes -- depending on the size and number of eggs.
Drain the pot.
Cool eggs immediately by running cold water over them or putting in iced water.
Crack and peel the eggs under very cold running water, starting by cracking the large (air pocket) end, then taking off the largest pieces first. Lowering the eggs' temperature keeps the shells from sticking, and prevents the greenish tinge sometimes seen on hard-boiled eggs. (The greenish tinge doesn't affect taste or safety, and does not indicate decay or toxicity. Instead, it is due to the reaction between iron and sulphur from the egg white and yolk.)