Bring a large pot of salted water to a boil. Add shell pasta and cook, stirring occasionally, until tender yet firm to the bite, about 9 minutes. Drain, run under cold water to cool pasta, and drain again.
Transfer drained pasta to a large bowl.
Add Asiago, salami, pepperoni, tomatoes, bell peppers, and olives. Sprinkle dry dressing mix over top and stir until ingredients are thoroughly mixed. Cover and refrigerate for at least 1 hour.
Make the dressing:
Whisk oil, vinegar, oregano, parsley, Parmesan, salt, and pepper together in a small bowl.
Cover and set aside until ready to serve.
When ready to serve, pour dressing over chilled salad and mix until well combined.