In a medium mixing bowl, whisk the Dijon mustard with the lemon juice, Worcestershire sauce, anchovy paste, and minced garlic until the ingredients are thoroughly blended. The anchovy paste should disperse completely throughout the mixture, providing the characteristic savory flavor associated with Caesar dressing.
Add the mayonnaise and stir until the dressing develops a smooth, creamy consistency. Fold in the finely grated Parmesan, then season with black pepper according to taste. Set the dressing aside while preparing the remaining ingredients so the flavors can combine.
Bring a large saucepan or pot of salted water to a rolling boil. Add the rotini or penne and cook according to the package instructions until al dente, which will generally take about 10 minutes. The pasta should be tender while retaining a slight firmness when bitten.
Drain the cooked pasta through a colander and give it a brief rinse under cool water to halt further cooking and wash away excess surface starch.
Arrange the pasta in a thin layer on a plate or sheet pan and allow it to cool for several minutes. Cooling it before assembly helps prevent the warm pasta from wilting the romaine.
While the pasta is cooling, shred the rotisserie chicken or cut it into pieces measuring roughly 1 inch. Remove the chicken skin if preferred.
Trim and chop the romaine hearts into manageable bite-size pieces, discarding any tough outer leaves. Rinse the lettuce thoroughly if necessary and have both the chicken and romaine ready for assembly.
Place the cooled pasta, prepared chicken, and chopped romaine in a large mixing bowl.
Pour the prepared Caesar dressing over the ingredients and toss thoroughly until the pasta, chicken, and lettuce are evenly covered. Scrape along the bottom and sides of the bowl as needed to distribute all of the creamy dressing throughout the salad.
Transfer the finished chicken Caesar pasta salad to a serving bowl or divide it among individual plates.
Add croutons if desired for extra crunch, then finish with an additional sprinkling of Parmesan cheese. Serve immediately, or refrigerate the salad until it is ready to be served.