Bring a large pot of water to a boil over high heat. Once boiling, add pasta and cook until al dente, about 8 to 9 minutes.
Drain pasta and add to a large bowl. Cool completely in the refrigerator, about 30 minutes.
In a small bowl, whisk together ingredients for the dressing.
Add mozzarella, tomatoes, peppers, basil, and parmesan to the pasta. Stir to combine.
Drizzle dressing over the pasta salad. Toss to combine, making sure everything is coated evenly.
Serve immediately or cover with plastic wrap and store for up to 1 to 2 days before serving.