Place your eggs in a pot and cover with cold water by 1 inch. Bring to a boil over medium-high heat, then cover, remove from the heat and set aside 8 to 10 minutes. Drain, cool in ice water and peel. How to Make Deviled Eggs:Transfer hard-boiled eggs to a bowl of ice water with a slotted spoon and let cool.lace your eggs in a pot and cover with cold water by 1 inch. Bring to a boil over medium-high heat, then cover, remove from the heat and set aside 8 to 10 minutes. Drain, cool in ice water and peel. How to Make Deviled Eggs: