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. This will make peeling easier.

Peel the cooled eggs and chop them into small pieces.

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

Toast the bread slices if desired.

Spread a generous amount of the egg salad mixture onto two slices of bread. Top with lettuce leaves if using, then place the remaining slices of bread on top to form sandwiches.

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