HARD-COOKED EGGS: PLACE eggs in saucepan large enough to hold them in single layer. ADD cold water to cover eggs by 1 inch. HEAT over high heat just to boiling. REMOVE from burner. COVER pan. LET EGGS STAND in hot water about 15 minutes for large eggs (12 minutes for medium eggs; 18 minutes for extra large). DRAIN immediately and serve warm. OR, cool completely under cold running water or in bowl of ice water, then REFRIGERATE.
Very fresh eggs can be difficult to peel. To ensure easily peeled eggs, buy and refrigerate them a week to 10 days in advance of cooking. This brief "breather" allows the eggs time to take in air, which helps separate the membranes from the shell. Hard-cooked eggs are easiest to peel right after cooling. Cooling causes the egg to contract slightly in the shell.