Preheat oven to 400°F (200°C) and line a baking sheet with parchment paper.
Place 1-tablespoon mounds of grated Parmesan cheese on the baking sheet, spaced 2 inches apart.
Bake for 5 minutes or until edges are golden and bubbly; remove and let cool completely to harden into crisps.
In a small mixing bowl, whisk together the mayonnaise, lemon juice, Dijon mustard, anchovy paste, Worcestershire sauce, minced garlic, salt, and pepper until smooth.
Place the chopped Romaine lettuce in a large chilled bowl.
Add 3 to 4 tablespoons of the dressing to the lettuce and toss thoroughly to ensure every leaf is coated.
Top the salad with shaved Parmesan and crumble the cooled Parmesan crisps over the top before serving.