Cook the pasta. Bring a large pot of salted water to a boil.
Cook pasta to al dente according to package directions. Drain and rinse under cool water to stop cooking and remove excess starch. Shake off water well.
Make the dressing. In a medium bowl, whisk together mayonnaise, Greek yogurt, lemon juice, Dijon, mashed anchovies, garlic, and Worcestershire.
Whisk in Parmesan, then stream in olive oil until creamy. Season with black pepper and a pinch of salt to taste.
Toss warm pasta with some dressing. In a large bowl, combine cooled pasta with about half the dressing. This helps the pasta absorb flavor without getting dry later.
Add chicken and extras. Fold in the chicken, cherry tomatoes, and red onion if using.
Add more dressing as needed to coat lightly but evenly.
Chill to set the flavors. Cover and refrigerate for 20–30 minutes if you have time. This step lets the flavors meld and the pasta fully absorb the dressing.
Add romaine and croutons just before serving. Gently fold in the chopped romaine and croutons so they stay crisp. Sprinkle in the remaining Parmesan.
Taste and finish. Add a squeeze of lemon, more pepper, or a pinch of salt if needed.
Serve with extra shaved Parmesan on top.