Dice both bell peppers into 1/2-inch pieces and thinly slice the red onion, then set aside in separate bowls. Halve the grape tomatoes lengthwise and drain the black olives, slicing them into rings. Chop the fresh parsley and set aside. Cut the mozzarella into bite-sized cubes or small chunks. Stack the pepperoni and salami slices and cut them into quarters or bite-sized pieces. Having everything prepped and ready will make assembly seamless once the pasta is cooked and cooled.
Bring a large pot of salted water to a boil and cook the rotini according to package directions until al dente—this is key for the right texture in a cold pasta salad, as overcooked pasta will turn mushy. Drain the pasta in a colander and rinse briefly with cold water to stop the cooking process. Spread the cooled pasta on a large baking sheet or into a wide bowl to help it cool faster and prevent clumping. I like to let it sit uncovered for a few minutes at room temperature before assembling, which helps prevent the pasta from being too cold and stiff when you mix everything together.
Transfer the cooled pasta from Step 2 into a large bowl or serving dish. Add all the prepped ingredients from Step 1: the diced red and green peppers, sliced red onion, halved tomatoes, sliced olives, cubed mozzarella, and the cut pieces of pepperoni and salami. Toss everything together gently but thoroughly to distribute all components evenly throughout the pasta, making sure the cheese and meats are well incorporated.
Pour the entire container of Italian dressing over the assembled salad and toss well until every piece of pasta and ingredient is coated with dressing. Once tossed, cover the bowl and refrigerate for at least 1-2 hours before serving to allow the flavors to meld together. For the best flavor, I recommend letting it chill overnight—the pasta absorbs the dressing beautifully and the flavors deepen considerably. Give it a gentle toss again just before serving and taste to adjust seasoning if needed.