Bring a large pot of salted water to a rolling boil. Add the cheese tortellini and cook according to package instructions until al dente, around 3-5 minutes. Drain the tortellini, rinse with cold water, and set aside to cool.

In a medium jar, combine 1/3 cup olive oil, 3 tablespoons red wine vinegar, 1 tablespoon Dijon mustard, 1 teaspoon honey, and 1 minced garlic clove. Add 1 teaspoon dried oregano and season with salt and pepper. Shake well until emulsified.

In a large mixing bowl, combine the cooled tortellini and pour half of the dressing over it. Gently mix to coat and let cool for about 10 minutes.

Add halved cherry tomatoes, diced cucumber, thinly sliced red onion, kalamata olives, mozzarella balls, chopped salami, grated Parmesan, spinach, and fresh basil. Drizzle remaining dressing and toss gently to combine.

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

Remove the salad from the refrigerator, give it a gentle toss, and garnish with additional fresh basil and a sprinkle of grated Parmesan. Serve chilled or at room temperature.