Cook the tortellini in a large pot of salted water according to package directions until al dente. Drain and rinse under cold water. Transfer to a large bowl.
While the tortellini cooks, make the dressing. In a jar with a tight-fitting lid, combine the olive oil, vinegar, mustard, honey, garlic, oregano, salt and pepper. Shake well until emulsified.
Pour half of the dressing over the warm tortellini and toss gently to coat. Let cool for 10 minutes.
Add the tomatoes, cucumber, red onion, olives, mozzarella, salami, Parmesan, spinach, and basil to the bowl with the tortellini. Pour the remaining dressing over the top and toss gently to combine all the ingredients.
Cover and refrigerate the salad for at least 2 hours to let the flavors meld. Toss again and taste for seasoning before serving. Add more salt, pepper, or vinegar if needed.
Garnish with additional fresh basil and Parmesan if desired. Serve chilled or at room temperature. Enjoy!