Step 1
Cook 8 oz. medium shell pasta in a medium pot of boiling salted water, stirring occasionally, until al dente. Drain well and let cool in colander (about 20 minutes).
Step 2
Meanwhile, purée 6 oil-packed anchovy fillets, 2 garlic cloves, 1 oz. Parmesan, finely grated (about ½ cup), ⅓ cup extra-virgin olive oil, 2 Tbsp. mayonnaise, 2 Tbsp. white wine vinegar, 2 Tbsp. fresh lemon juice, and 1 tsp. freshly ground pepper in a blender until smooth and creamy. Season dressing with kosher salt. (Alternatively you can finely chop anchovies and garlic, then whisk with remaining ingredients in a medium bowl to make the dressing.)
Step 3
Place 3 heads of Little Gem lettuce or 2 romaine hearts, leaves separated, torn if large, in a large bowl. Drizzle lightly with lemon juice, add a small pinch of salt, and season with pepper. Toss leaves gently to coat.
Step 4
Add 1 cup shredded skinless rotisserie chicken breast and reserved pasta to lettuce and drizzle dressing over. Using your hands, gently toss to combine.
Step 5
Transfer salad to a platter and top with shaved Parmesan.
