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 it 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, salt, black pepper, and finely chopped dill pickles. Mix gently until well combined.
Toast the bread slices until golden brown.
Divide the egg salad evenly between two slices of toasted bread.
Top the egg salad with shredded iceberg lettuce.
Place the remaining bread slices on top to form sandwiches.
Cut each sandwich in half and serve immediately.