Place eggs in a single layer in an extra-large saucepan or Dutch oven (do not stack eggs). Add enough cold water to cover the eggs by at least 1 inch. 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. (If you have extra-large eggs, let them stand in the boiled water for 18 minutes.) 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.
Prepare stuffed eggs as directed. Place in an airtight container and chill in the refrigerator for up to 24 hours.