In a large pot, bring salted water to a rolling boil over high heat. Add the tortellini and cook according to package instructions, usually about 3–5 minutes, until they are al dente and float to the surface. Drain and briefly rinse under cold water to cool.

While the tortellini cools, combine olive oil, red wine vinegar, Dijon mustard, honey, minced garlic, and dried oregano in a jar. Season with salt and pepper. Secure the lid and shake vigorously for about 30 seconds.

Transfer cooled tortellini to a mixing bowl. Pour half of the dressing over the tortellini and gently toss. Set aside for 10 minutes.

Add cherry tomatoes, cucumber, red onion, kalamata olives, mozzarella, salami or pepperoni, Parmesan, spinach or arugula, and basil into the bowl. Drizzle remaining dressing over and toss until combined.

Cover the bowl with plastic wrap or a lid and place in the refrigerator for at least 2 hours.

Once chilled, toss the salad again and adjust seasoning with salt and pepper as needed. Serve chilled or at room temperature.