Cook pasta in salted water according to directions on package. Reserve 1/2 cup pasta cooking water and set aside to cool. Drain pasta then transfer to an 18 by 13-inch rimmed baking sheet that's sprayed with non-stick cooking spray or lined with parchment paper and let cool completely.
Mince anchovies and place in a medium mixing bowl, mash to a paste with the back of a spoon. Add in mayonnaise, lemon juice, parmesan, dijon mustard, Worcestershire sauce, garlic, and salt and pepper to taste. Whisk to blend. Chill in fridge until ready to use.
Add cooled pasta, lettuce, chicken, tomatoes, and parsley to a large salad bowl. Pour dressing over top and toss to evenly coat, thin mixture with pasta water as needed (it will thicken as it sits).
Add croutons and parmesan and toss a few times to incorporate.
