Soft-boiled (oeufs coques) and medium-soft-boiled eggs (oeufs mollets) should be served immediately.
Hard-boiled eggs (oeufs durs) should be transferred immediately to ice water to set until completely cool and to prevent a gray-green ring from forming around the firm yolk. Chill until completely cold.
To facilitate peeling for hard-boiled eggs, you can lift the warm eggs from the chilling water, crack the shells slightly, and return them to the cold water until completely cold. When chilled, the shell should peel right off.