Cook the pasta: Bring a large pot of salted water to boil. Add pasta and cook according to package directions until al dente. Drain and rinse with cold water to stop cooking process. Set aside to cool completely.
Prepare the dressing: In a small bowl, whisk together olive oil, red wine vinegar, minced garlic, oregano, salt, and pepper until well combined.
Prepare the vegetables: While pasta cools, halve the cherry tomatoes, slice the red onion, chop the sun-dried tomatoes, and slice the olives. Chop the fresh basil and parsley.
Assemble the salad: In a large mixing bowl, combine the cooled pasta, cherry tomatoes, mozzarella balls, red onion, olives, and sun-dried tomatoes.
Add dressing and herbs: Pour the dressing over the pasta mixture and toss gently to coat. Add the fresh basil and parsley, then toss again.
Add cheese: Sprinkle the Parmesan cheese over the salad and give it a final gentle toss.
Chill and serve: Cover and refrigerate for at least 1 hour before serving to allow flavors to meld. Serve chilled. Can be stored in refrigerator for up to 3 days.