Prepare the dressing by whisking together mayonnaise, Parmesan, lemon zest, lemon juice, garlic, Dijon mustard, black pepper, and Worcestershire sauce until smooth.
Cook the pasta according to package instructions, then drain and let it cool.
In a large bowl, combine the cooked pasta, chopped lettuce, chicken, cherry tomatoes, and avocado if using.
Pour the dressing over the salad and toss gently until everything is evenly coated.
Sprinkle shaved Parmesan on top and add optional toppings before serving.