While the anchovies add a deeper flavor to the salad, feel free to omit them if you don't like fish.
Heat a cast-iron grill pan. Brush cut sides of the romaine with olive oil. Generously sprinkle with salt and pepper. Grill until charred and blackened in a few places, about 2 minutes.
Place the lettuce pieces on a platter. Drizzle with olive oil, lemon juice, and shaved Parmesan. Garnish with anchovies, if desired.