Boil a large pot of salted water. Add tortellini and cook according to package instructions for 3–5 minutes until they float and are tender. Drain and rinse with cold water, then set aside to cool.

In a mixing bowl, combine the cooled tortellini, cherry tomatoes, mini pepperoni, black olives, mozzarella, and jarred roasted red peppers. Stir gently.

In a small bowl, whisk together the roasted red pepper oil, olive oil, balsamic vinegar, red wine vinegar, and Parmesan cheese until smooth. Adjust the flavor as desired.

Pour the dressing over the salad mixture and toss until all ingredients are coated with the dressing.

Season with salt and pepper to taste. Cover and refrigerate for at least one hour to allow flavors to meld.

Before serving, stir the salad and garnish with freshly chopped basil.