Whisk together Dijon mustard, lemon juice, Worcestershire sauce, mayonnaise, garlic, and anchovy paste in a bowl until smooth.
Stir in Parmesan cheese and black pepper; set dressing aside.
Cook pasta in salted water until al dente (about 10-12 minutes), then drain and rinse with cold water.
Transfer cooled pasta to a large serving bowl.
Chop Romaine hearts into 1-inch pieces and add to the bowl with pasta.
Add shredded chicken to the bowl.
Pour dressing over ingredients and toss until well coated.
Add croutons if using and sprinkle with additional Parmesan cheese before serving.