Preheat your grill to medium-high heat, around 375 to 400ºF. This will ensure the perfect temperature for grilling the lettuce.
In a small bowl, whisk together the minced anchovy fillets, minced garlic cloves, mayonnaise, Worcestershire sauce, Dijon mustard, olive oil, finely grated Parmesan cheese, and lemon juice. Season with salt and pepper to taste. This flavorful dressing will complement the grilled lettuce perfectly. Set it aside.
Cut the romaine lettuce hearts in half lengthwise. This will make them easier to handle and allow for even grilling.
Brush the cut side of the romaine lettuce with olive oil and sprinkle with salt and pepper. This will enhance the flavors and ensure a deliciously seasoned result.
Place the lettuce halves on the preheated grill, and cut the side down. Gently press down on the lettuce to ensure direct contact with the grill grates.
Grill the lettuce for 1-2 minutes or until it becomes slightly charred. Then, flip the lettuce over and grill for an additional 1-2 minutes. This quick grilling process will add a smoky flavor and a nice texture to the lettuce.
Serve the grilled romaine lettuce with Caesar dressing immediately to enjoy it at its best. The combination of smoky, charred lettuce and creamy dressing is simply irresistible.