In a large mixing bowl, combine the shredded chicken, romaine lettuce, cherry tomatoes, red onion, cucumber, and mozzarella cheese.

In a separate small bowl, whisk together the mayonnaise, Dijon mustard, lemon juice, salt, and pepper until smooth.

Pour the dressing over the chicken mixture and toss gently until everything is well coated.

Slice the sandwich rolls in half and lightly toast them if desired.

Spoon the chicken salad mixture onto the bottom half of each roll and top with fresh basil leaves.

Place the top half of the roll on the sandwich and serve immediately.