Bring a large saucepan of water to a boil over medium-high heat. Using a slotted spoon, carefully lower eggs into water one at a time. Cook 6½ minutes (I prefer 6), adjusting heat to maintain a gentle boil. Transfer eggs to a bowl of ice water and chill until just slightly warm, about 2 minutes.
Gently crack eggs all over and peel, starting from the wider end, which contains the air pocket.
Do Ahead: Eggs can be cooked and peeled 3 days ahead. Store airtight in the refrigerator.