Place the eggs in a pot and cover them with water, ensuring they are submerged. Bring to a boil, then cover and remove from heat, letting them sit for about 10 minutes to cook through.

Transfer the eggs to a bowl of ice water for about 5 minutes.

Once cooled, gently tap the eggs on a hard surface and peel under running water.

Using a sharp knife, chop the peeled eggs into small pieces.

In a mixing bowl, combine the chopped eggs, mayonnaise, Dijon mustard, chopped celery, and green onions. Stir until well combined.

Add salt and pepper to taste, mixing well after each addition.

If using whole loaves, slice the bread to your desired thickness.

Spread a generous amount of the egg salad on one slice of bread, topping with lettuce if desired. Place another slice on top and cut in half.