To hard-cook eggs, place them 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 and let eggs stand in hot water about 15 minutes for large eggs (12 minutes for medium eggs; 18 minutes for extra-large) Cool completely under cold running water and peel.
Hard-cooked eggs are easiest to peel right after cooling, which causes the egg to contract slightly in the shell. To peel a hard-cooked egg, gently tap egg on countertop until shell is finely crackled all over. Roll egg between hands to loosen shell. Starting peeling at large end, holding egg under cold running water to help ease the shell off.