Place chicken in a gallon resealable storage bag; whisk together olive oil, mustard, garlic, salt and pepper; add to the bag and toss; refrigerate 1-24 hours.
Remove chicken from refrigerator; set out 30 minutes.
Place oven rack ~4 inches from broiler coil; set oven to broil; butter the inside of each bun; place butterside-up on a foil lined broiler pan; broil ~3 minutes, until lightly toasted; set aside.
Remove chicken from marinade; place on the same broiler pan; broil each side ~5 minutes, or until the internal temperature reaches 165°F.
Sprinkle with lemon juice and Parmesan, if you wish.
Slice each roll, if not already sliced, then spread dressing on the interior sides of each roll.
Place cooked chicken breasts on the bottom half of each roll, with lettuce above and below; complete each with the top.
Serve with lemon wedge and Parmesan, if you wish.