In a small bowl, whisk together balsamic vinegar, Dijon mustard, honey, and dried oregano until combined. While whisking, slowly drizzle in extra-virgin olive oil to create a smooth, emulsified dressing. Season with salt and pepper to taste, and set aside.

Bring a pot of salted water to a boil. Add short pasta and cook until al dente, about 8-10 minutes. Drain and rinse under cold running water to cool.

In a large mixing bowl, combine cooled pasta, fresh mozzarella, diced peaches, and halved cherry tomatoes. Gently add arugula and freshly chopped basil. Pour the balsamic dressing over the mixture and toss until evenly coated.

Toss the salad thoroughly to mix and coat ingredients. Cover and refrigerate for at least 30 minutes to allow flavors to meld.

Before serving, give the salad a gentle toss and serve in a large bowl or individual plates, garnished with extra basil if desired.