In a jar with a tight-fitting lid, combine the red wine vinegar, Dijon mustard, oregano, Italian seasoning, sugar, olive oil, mayonnaise, salt, and pepper. Shake well until smooth. Refrigerate while preparing the salad.
Bring a large pot of salted water to a boil.
Cook the pasta according to the package directions until al dente.
Drain the pasta and rinse under cold water for about 20 seconds. Drain well.
While the pasta cools, chop the chicken, turkey salami, cherry tomatoes, roasted red peppers, cucumber, parsley, olives, and red onion.
In a large mixing bowl, combine the cooled pasta, chicken, turkey salami, vegetables, parsley, olives, and Parmesan cheese.
Pour the dressing over the salad and toss until everything is evenly coated.
Taste and adjust with additional salt and black pepper if needed.
Refrigerate the Italian Pasta Salad Recipe for at least 10 minutes before serving.
Toss once more before serving and enjoy chilled.