01 - Heat grill or grill pan to medium-high temperature, approximately 375°F to 400°F.
02 - Rub chicken breasts thoroughly with olive oil, then coat evenly with salt, black pepper, and garlic powder on all sides.
03 - Place chicken on preheated grill and cook for 6 to 7 minutes per side until internal temperature reaches 165°F and juices run clear. Remove from heat and let rest for 5 minutes before slicing thinly across the grain.
04 - While chicken grills, whisk together mayonnaise, grated Parmesan, lemon juice, Dijon mustard, Worcestershire sauce, and minced garlic in a small bowl until smooth and well combined.
05 - Spread softened butter generously on cut sides of each roll. Place butter-side down on grill or in skillet and toast until golden brown and crispy, about 2 to 3 minutes.
06 - Spread a layer of Caesar dressing on bottom half of each toasted roll. Layer with shredded romaine, sliced grilled chicken, shaved Parmesan, and cherry tomatoes. Top with remaining roll half.
07 - Slice each sandwich diagonally in half and serve immediately while warm.