Bring a large pot of salted water to a boil and cook the fusilli according to package directions until just past al dente—this gives the pasta enough texture to absorb the dressing without becoming mushy. Drain thoroughly and immediately toss with the olive oil to prevent sticking. Spread the pasta on a large cutting board or sheet pan to cool to room temperature, stirring occasionally so it cools evenly. This step typically takes 15-20 minutes and can happen while you prep the vegetables.
While the pasta cools, prep all your vegetables to save time during assembly. Halve the cherry tomatoes, dice the red pepper into bite-sized pieces, slice the cucumber into 1/4-inch half moons, finely dice the red onion, and slice both the kalamata olives and pepperoncini into thin rings. Chop the fresh parsley and tear the fresh basil into small pieces. I like to keep the basil separate from the other herbs since it's more delicate and tastes fresher when added just before serving. Have the mozzarella pearls and grated parmesan ready as well.
Once the pasta has cooled to room temperature, transfer it to a large mixing bowl. Add the prepared tomatoes, mozzarella pearls, red pepper, cucumber, red onion, olives, and pepperoncini along with the chopped parsley. Pour in the Italian dressing and season with kosher salt and freshly cracked black pepper. Toss everything together thoroughly, ensuring the dressing coats all the pasta and vegetables evenly. I recommend letting this sit for 10-15 minutes before serving so the flavors can meld together and the pasta can fully absorb the dressing.
Just before serving, gently fold in the torn fresh basil and top with the grated parmesan cheese. This keeps the basil bright and prevents it from bruising or darkening. Give the salad one final gentle toss to distribute the basil evenly, then transfer to a serving bowl or individual plates. The salad tastes best served at room temperature and can be made up to 2 hours ahead—just add the basil and parmesan right before serving for the best flavor and texture.