In a large pot, bring salted water to a rolling boil. Add the cheese tortellini and cook for about 5 minutes, or until they float and are al dente. Drain and rinse under cold water.

In a mixing bowl, add the chilled tortellini. Drizzle the basil pesto over the pasta and toss to coat. Add fresh mozzarella, halved tomatoes, chopped basil, and red onion, stirring gently.

Cover with plastic wrap or transfer to an airtight container. Refrigerate for 30 minutes to 1 hour to allow flavors to meld. Stir gently before serving.