Season romaine with olive oil and S&P. Place cut side down on hot grill for 1 minute.
Quarter turn and grill for another minute. Flip lettuce, grill 1 last minute.
On a plate pour Caesar dressing across the center. Place sliced tomatoes across the dressing.
Place one half romaine pointing toward plate corner. Lean other half romaine on first one at the base, facing a quarter turn away. Place white anchovies across both halves of lettuce. Spread shredded parmesan generously throughout. Serve immediately.