In a medium bowl whisk together ¼ cup mayonnaise, 2 tablespoons lemon juice, 1 tablespoon anchovy paste, 1 teaspoon dijon mustard, ½ teaspoon minced garlic, ½ teaspoon kosher salt, and ¼ teaspoon ground black pepper. Slowly whisk in ½ cup extra-virgin olive oil until a thickened dressing is formed. Whisk in ¼ cup grated parmesan cheese.
Preheat the grill to medium-high heat (350 to 400 degrees Fahrenheit). Carefully grease the grates using tongs to rub them with a paper towel dipped in olive oil.
Use a pastry brush or silicone brush to brush olive oil on the cut sides of 2 hearts quartered romaine. Lightly season with salt.
Place the lettuce with one cut side down on the grill, pressing it down so it creates direct contact with hot grates. Cook until lightly charred, about 1 to 2 minutes.
Flip to the other cut side and grill 1 to 2 additional minutes. Transfer grilled lettuce to serving plates.
Drizzle the grilled lettuce with the Caesar dressing and top with ground black pepper, ⅓ cup freshly grated parmesan cheese, and 1 cup croutons. Serve immediately.
