Fill the pot with water. Add some salt. Bring to a boil. Add rotini to the salted boiling water. Cook according to the package directions. Drain and rinse under cold water. Transfer chilled cooked rotini to the large salad bowl.
Add Castelvetranos olives, Kalamata olives, sun-dried tomatoes, mozzarella cheese, and parmesan cheese to the bowl with rotini. Set aside.
In a small bowl, mix together olive oil, sun-dried tomato oil, red wine vinegar, garlic, dijon mustard, honey, red pepper flakes, salt, and pepper.
Add oily dressing to the pasta salad. Stir until completely coated. Store this salad in the refrigerator before serving.