Place the eggs in a single layer in a saucepan and cover with cold water by about an inch.
Bring the water to a boil over medium-high heat. Once boiling, cover the saucepan, remove from heat, and let the eggs sit for 10 minutes.
Drain the hot water and transfer the eggs to a bowl of ice water to cool for 5 minutes.
Peel the cooled eggs and chop them into small pieces.
In a medium bowl, combine the chopped eggs, mayonnaise, Dijon mustard, chopped chives, salt, and black pepper. Mix until well combined.
Fold in the finely chopped dill pickles gently.
Toast the bread slices until lightly golden.
Divide the egg salad mixture evenly onto two slices of toasted bread.
Top each with lettuce leaves and cover with the remaining bread slices to form sandwiches.
Cut the sandwiches in half and serve immediately.