Place eggs in a single layer in saucepan. Add enough water to come to at least 1-inch above eggs. Quickly bring to boiling and turn off heat.
Remove pan from burner. Let eggs stand, covered, in hot water 15 minutes for large eggs (12 minutes for medium, 18 minutes for extra large).
Immediately run cold water over eggs or place them in ice water until completely cooled (about 15 minutes).
To remove shell, crack it gently by tapping egg all over on hard surface. Roll egg between hands to loosen shell.
Start peeling at large end. Hold egg under running cold water or dip in a bowl of water to help ease off shell.
Refrigerate hard-cooked eggs in their shells and use them within 1 week.