Add the vinegar, Dijon mustard, oregano, Italian seasoning, sugar, olive oil, mayonnaise, salt, and pepper to a jar with a tight-fitting lid. Shake well until smooth. Refrigerate until ready to use.
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. Allow excess water to drain completely.
Chop the chicken, halal beef salami, tomatoes, cucumber, roasted red peppers, olives, parsley, and red onion.
Add the cooked pasta, chicken, beef salami, vegetables, parsley, and Parmesan cheese to a large mixing bowl.
Pour the dressing over the salad and toss until evenly coated. This Italian Pasta Salad Recipe tastes best when every ingredient is well coated.
Taste and adjust with additional salt and black pepper if needed.
Refrigerate for 10 minutes before serving. Toss again just before serving.