Bring a pot of salted water to a rolling boil. Add the cheese tortellini and cook according to package instructions, about 3-5 minutes, until al dente. Drain and rinse under cold water.

In a jar, combine olive oil, red wine vinegar, Dijon mustard, honey, minced garlic, and oregano. Season with salt and pepper. Secure the lid and shake for 30 seconds until emulsified.

Place the cooled tortellini in a large mixing bowl and drizzle half of the dressing over it. Toss gently to coat and let cool for 10 minutes.

Add cherry tomatoes, cucumber, red onion, olives, mozzarella, salami/pepperoni (if using), Parmesan, spinach, and basil to the tortellini. Toss gently to combine.

Cover and refrigerate for at least 2 hours to allow flavors to meld. Adjust seasoning with salt, pepper, or more dressing before serving.

Toss again before serving. Serve chilled or at room temperature, garnishing with extra basil and Parmesan.