"Old" eggs peel more easily than fresh ones. If your eggs are right off the farm, you may have a hard time peeling them. So if you're planning on deviled eggs for a crowd, it's smart to buy your eggs ahead and hold them in your fridge for at least week before cooking them.
Place the eggs into a deep saucepan or Dutch oven and cover by 2 inches with cool tap water.
Place the pan over high heat and bring the eggs to a boil. Turn off the heat and cover the pan.
Let the eggs sit in the hot water for 8-10 minutes. Drain the water and give the pan a shake to crack each egg a little bit. Fill the pan with cold tap water to cool the eggs off.
Peel immediately or store in the refrigerator for up to a week.