Bring a large pot of salted water to a boil. Add 20 ounces of cheese tortellini and cook according to package directions until al dente. Drain and rinse under cold water. Place the tortellini in a large bowl and drizzle with a bit of olive oil; stir to prevent them from sticking together.
In a small mixing bowl, stir ½ basil pesto and 2 tablespoons of the jarred pepperoncini brine. Set aside
In the large mixing bowl with the tortellini, add the halved grape tomatoes, pepperoncini slices, halved kalamata olives, and the mozzarella cheese pieces.
Pour the basil pesto and brine mixture over the pasta salad and gently toss to combine.
Season with Kosher salt and fresh ground black pepper, and garnish with basil leaves.
Can be made up to 8 hours in advance.