If serving eggs cold, add 1 tray of ice cubes to a large bowl and fill with water.
Add 1 inch of water to a large pot. Place steamer insert inside, cover, and bring to a boil over high heat. Add eggs to steamer basket, cover, and continue cooking, 7 minutes for soft-boiled eggs or 14 minutes for hard-boiled.
Serve immediately if serving hot. If serving cold, immediately place eggs in bowl of ice water and allow to cool for at least 15 minutes before peeling.
To peel, first gently tap hard-boiled eggs all over to thoroughly crack the shell, then remove shell under a thin stream of running water. (The water helps get under the shell and lift it off the egg.)