Place the eggs in a saucepan and cover them with cold water. Bring to a boil over medium-high heat. Once boiling, cover the pot and remove it from heat. Let it sit for 12 minutes.
After 12 minutes, transfer the eggs to a bowl of ice water to cool for about 5 minutes. Once cooled, peel the eggs and chop them into small pieces.
In a mixing bowl, combine the chopped eggs, mayonnaise, Dijon mustard, salt, pepper, chives, and dill (if using). Mix until well combined.
Slice the dinner rolls in half and place a lettuce leaf on the bottom half of each roll.
Spoon a generous amount of egg salad onto the lettuce and top with the other half of the roll.
Serve immediately or refrigerate for up to 2 hours before serving.