Cook pasta according to package directions until al dente; drain and cool under cold water.
In a large bowl, combine pasta, salami, pepperoni, mozzarella cheese, black olives, bell peppers and tomatoes. Stir in Italian dressing mix. Cover and refrigerate at least 1 hour.
To prepare the dressing, whisk together olive oil, balsamic vinegar, oregano, parsley, Parmesean cheese, and salt and pepper to taste.
Pour dressing over pasta salad just before serving.