Hard-boil the eggs by placing them in a pot, covering with water, and bringing to a boil.
Cover the pot and remove it from heat, letting the eggs sit for 10-12 minutes.
Peel the eggs and chop them into small pieces.
In a bowl, combine chopped eggs with mayonnaise and Dijon mustard.
Add fresh dill, salt, and pepper, stirring until well mixed.
Lay out slices of bread on a clean surface.
Place a layer of lettuce on one slice of bread.
Spoon the egg salad mixture generously over the lettuce.
Top with tomato and onion slices if desired.
Place the second slice of bread on top, cut in half, and serve.