Whisk together Dijon mustard, lemon juice, Worcestershire sauce, mayonnaise, garlic, and anchovy paste until smooth. Stir in the grated Parmesan and a pinch of black pepper. Set the dressing aside so the flavors blend while you prepare the rest.
Bring salted water to a boil and cook your pasta until al dente. Drain well, then add the warm pasta to a large mixing bowl. The slight warmth helps the pasta absorb more of the dressing later.
Chop the Romaine into bite-sized pieces and add it to the bowl with the pasta. Mix in the shredded chicken, then pour the dressing over everything. Toss gently until well coated. Add croutons and extra Parmesan right before serving.