Bring a large pot of salted water to a boil over high heat. Add the tortellini and cook according to package instructions, usually around 3–5 minutes. Drain and let cool.

In a large mixing bowl, combine the cooled tortellini with the pesto sauce, Genoa salami, artichoke hearts, and diced bell peppers. Toss until well-coated.

Grate a generous amount of Parmigiano Reggiano over the salad mixture and fold in evenly.

Cover and place in the refrigerator for at least 30 minutes to 1 hour.

Remove from the fridge, toss gently, and serve. Top with additional grated cheese if desired.