Bring a pot of generously salted water to boil and cook the fusilli per package instructions. Drain and set aside.
Whisk together the oil, vinegar, oregano, honey, 2 tablespoons Parmesan and salt and pepper in a large bowl. Add the warm pasta, then toss to coat and sprinkle with the remaining 2 tablespoons Parmesan. Add the artichokes, red peppers, olives, mozzarella and salami and toss well to combine. Sprinkle with fresh basil.