Preheat the oven to 400°F (204°C). Slick a rimmed baking sheet with oil.
Rinse the romaine lettuce. Drain and then pat it completely dry. Slice each head in half lengthwise and place the halves on the baking sheet, cut side up.
In a small bowl, whisk together the anchovy paste, garlic, and olive oil, until smoothly blended. Divide the anchovy mixture among the romaine halves and use a pastry brush to coat the lettuce. Sprinkle with black pepper.
Bake until the lettuce is wilted and brown at the edges, 8 to 13 minutes, depending on the size of the lettuce heads.
Immediately sprinkle with the shaved Parmesan, if desired, and serve right away.