Place the eggs in a medium saucepan and cover with cold water by about an inch.
Bring the water to a boil over medium-high heat. Once boiling, cover the pan, remove from heat, and let sit for 10 minutes.
Drain the hot water and transfer the eggs to a bowl of ice water. Let 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 until well combined.
Toast the slices of whole wheat bread until golden brown.
Place a leaf of romaine lettuce on two slices of the toasted bread.
Divide the egg salad mixture evenly over the lettuce leaves.
Top with the remaining bread slices to form sandwiches.
Cut each sandwich in half and serve immediately.