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 10 minutes, maintaining a gentle boil. Carefully transfer eggs to a bowl of ice water and let cool until just slightly warm, about 2 minutes.
Gently crack eggs all over and peel, starting from the fat end containing the air pocket.
Do Ahead: Eggs can be cooked and peeled 3 days ahead. Transfer to an airtight container and chill.