This is the best technique for cooking eggs so they're easy to peel. The consistent heat of the steam paired with immediate cooling in the ice bath makes them a cinch to peel.
Place a steamer basket in a saucepan with 1" water, bring water to a boil over medium-high heat. When the water comes to a full boil, add eggs. Cover and steam for 12 minutes for hard-cooked eggs, 7 minutes for soft-cooked.
While eggs are cooking, fill a medium bowl with ice and water. Remove eggs from pan and place in an ice bath. Peel when cooled enough to handle.
Notes
If not using right away, peel eggs and place in a container with water to cover along with a slice of lemon or 1 tablespoon of lemon juice.