Place the eggs in a saucepan and cover them with cold water. Bring the water to a boil over medium-high heat. Once boiling, cover the pan, remove it from heat, and let it sit for 12 minutes.

After 12 minutes, transfer the eggs to a bowl of ice water to cool for about 5 minutes. Once cooled, peel the eggs and chop them into small pieces.

In a mixing bowl, combine the chopped eggs, mayonnaise, Dijon mustard, lemon juice, salt, pepper, celery, and green onion. Stir until well mixed.

Taste and adjust seasoning if necessary. If you prefer a creamier texture, add more mayonnaise.

To assemble the sandwiches, spread a generous portion of the egg salad onto 4 slices of bread. Top with lettuce and tomato slices if desired, then place the remaining slices of bread on top.

Cut the sandwiches in half and serve immediately, or wrap them in plastic wrap and refrigerate for up to 2 hours before serving.