In a small bowl, whisk balsamic, mustard, honey, and oregano. Drizzle in olive oil, whisking until dressing is smooth. Season with salt and pepper to taste and set aside.
Pasta Salad
Cook pasta in boiling water until al dente. Drain pasta, rinse in cold water to cool, and place in a large bowl.
Add mozzarella, peaches, cherry tomatoes, arugula, basil, and balsamic dressing to pasta and toss well until evenly coated. Season salad with salt and pepper to taste and refrigerate until ready to serve.