Bring a large pot of generously salted water to a boil.
Cook the elbow macaroni until al dente according to package directions.
Drain, rinse under cold water, and allow the pasta to drain thoroughly.
Transfer the pasta to a large serving bowl.
Toss with 2 tablespoons of olive oil.
Add the rotisserie chicken, cucumber, cherry tomatoes, olives, roasted peppers, beef salami, red onion, and parsley.
Season lightly with kosher salt.
In a small bowl, whisk together the remaining olive oil and red wine vinegar.
Pour the dressing over the salad.
Toss until everything is evenly coated.
Sprinkle with ricotta salata or feta cheese.
Let the Italian Chicken Pasta Salad rest at room temperature for about 30 minutes before serving for the best flavor.