Bring a large pot of salted water to a rolling boil, then add the cheese tortellini. Cook according to package instructions until al dente, usually around 3 to 5 minutes. Drain and rinse under cold running water. Set aside to cool.

While the tortellini cool, slice the quartered artichoke hearts and thinly slice the red onion. Shred the parmesan cheese and chop the fresh basil. If making homemade pesto, prepare it now.

In a large mixing bowl, combine the cooled tortellini, mozzarella pearls, sliced artichokes, sun-dried tomatoes, shredded parmesan, chopped basil, and red onion. Pour in the pesto and toss until well-coated.

Cover with plastic wrap and refrigerate for at least 30 minutes before serving to allow flavors to meld. Toss again before serving and garnish with extra parmesan and fresh basil if desired.