Place eggs into a pot, and cover with water. Bring the eggs to a boil on the stove top, once the water is boiling, place a lid on the pot, and turn off the heat. Allow the eggs to sit for 10 minutes, they will cook themselves with the residual heat in the pot.
Overcooking boiled eggs gives you green eggs and that never looks attractive. After ten minutes, remove the pot from the stove top, and allow the faucet to pour cool water over the eggs. Once the water is no longer hot, add a few ice cubes, and let the eggs cool.
When the eggs have cooled, peel the eggs and then give them a rough chop and place into a bowl. Combine chopped eggs along with the mayonnaise and black pepper. Options: You can add your own variety of extra ingredients, maybe you would like some dill pickle or even some onion to the egg salad for a different flavor. I really enjoy egg salad on toasted sourdough bread.