To hard-cook eggs: Place eggs in a single layer in a medium saucepan. Add enough cold water to just cover the eggs. Bring to a rapid boil over high heat (water will have large rapidly breaking bubbles). Remove from heat, cover, and let stand for 15 minutes; drain. Run cold water over the eggs or place them in ice water until cool enough to handle; drain. To peel eggs, gently tap each egg on the countertop. Roll the egg between the palms of your hands. Peel off eggshell, starting at the large end. Cover and store in the refrigerator for up to 3 days.