Put a rubber band around your egg carton and store it on its side for at least 24 hours. This will help to center the yolks for slicing and for deviled eggs.
Put eggs in a heavy saucepan and cover with cold water. Use a large enough pan so that all of the eggs are in one layer. There should be an inch or more of water covering the eggs. Add 1 T. salt.
Put the eggs in cold water on the stove on high heat; bring the water and eggs to a boil.
When the eggs come to a boil, remove the pan from the heat and cover with a tight-fitting lid. Let sit for 15 minutes. If your pan is not a heavy one, the eggs may need to sit in the hot water for 2 or 3 extra minutes.
Prepare an ice bath, which is a large bowl filled with water and ice.
Drain the eggs. Remove them with a slotted spoon into the ice bath. Leave eggs in the ice bath until they are cool enough to handle.
To peel, crack eggs evenly all over and roll gently on a hard surface. Remove peel and membrane. Eat with a bit of good butter, sea salt and pepper.
If you plan to use the eggs in a salad, refrigerate for at least an hour prior to slicing.
If you decide to store some or all of the hard-cooked eggs for later consumption, store in the refrigerator in a covered container. Use within five days.