Cook tortellini in boiling salted water according to package directions until al dente. Drain and rinse under cold water.
In a large bowl, mix together basil pesto and pepperoncini brine until well combined.
Add the cooled tortellini to the pesto mixture and toss gently to coat.
Fold in artichoke hearts, mozzarella cheese, salami strips, cherry tomatoes, pepperoncini peppers, red onion, and Kalamata olives if using.
Season with salt and pepper to taste, and garnish with fresh parsley if desired.
Refrigerate for at least 30 minutes before serving to allow flavors to meld.