Place the eggs in a saucepan and cover them with water.
Bring the water to a boil, then reduce the heat and simmer for 10 minutes.
Drain the hot water and transfer the eggs to a bowl of cold water. Once cool, peel and chop the eggs.
In a mixing bowl, combine the chopped eggs, mayonnaise, Dijon mustard (if using), lemon juice, salt, and black pepper.
Mix well until all the ingredients are thoroughly combined.
Stir in the chopped parsley or chives.
Butter the bread slices if desired.
Toast the bread slices in a toaster or on a griddle until golden brown.
Spread the egg mayo mixture evenly over two slices of bread.
Top with the remaining slices of bread.
Cut the sandwiches in half and serve immediately.