Pour both jars of Rao’s Homemade roasted peppers (including the pine nuts, raisins, and oil) into a large bowl. Use a spoon to break any large peppers into 1-inch pieces.
Place the olives on a cutting board and gently smash them with the side of a chef’s knife. Add the olives, along with any juices that have accumulated on the board, to the bowl with the peppers. Julienne about half the basil leaves and add them to the bowl, along with the tomatoes, vinegar, garlic, and red pepper flakes, and toss well. Set aside to marinate at room temperature for 30 minutes to 1 hour, tossing occasionally
Meanwhile, bring a large pot of salted water to a boil. Add the pasta and cook for 9 to 11 minutes, stirring occasionally, until tender. Drain and immediately add to the bowl with the vegetables, along with 1½ teaspoons salt. Toss well, then set aside to cool completely.
Julienne the remaining basil leaves and add them to the pasta, along with the mozzarella and salami or prosciutto, if using. Toss well and season to taste with salt, black pepper, and red pepper flakes.
Serve immediately or refrigerate for up to 3 days. Bring the pasta salad room temperature before serving.