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.

In a jar with a tight-fitting lid, combine 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.

Toss in the tomatoes, cucumber, red onion, olives, mozzarella, salami, Parmesan, spinach, and basil. Pour in the remaining dressing and gently combine.

Cover and refrigerate the salad for at least 2 hours to let the flavors meld. Toss again and taste for seasoning before serving; adjust with more salt, pepper, or vinegar if needed.

Garnish with extra fresh basil and Parmesan if desired. Serve chilled or at room temperature.