Cook tortellini according to package directions. Drain and rinse under cold water. Set aside to cool completely.
In a large bowl, combine the cooled tortellini, tomatoes, olives, peppers, red onion, salami, and cheese.
Add the pesto and toss everything to coat. If the pesto is too thick, drizzle in olive oil to loosen it.
Season with salt and pepper to taste.
Refrigerate for at least 30 minutes before serving to let flavors meld.
Garnish with fresh basil if desired, and serve chilled or at room temperature.