In a small bowl, whisk together balsamic vinegar, Dijon mustard, honey, and dried oregano. Slowly drizzle in olive oil until emulsified. Season with salt and pepper and set aside.

Bring a large pot of salted water to a boil. Cook the pasta until al dente, then drain and rinse under cold water.

In a large mixing bowl, combine the cooled pasta, diced mozzarella, diced peaches, and halved cherry tomatoes. Gently fold in arugula and chopped basil. Pour the dressing over the mixture and toss to coat.

Taste and adjust seasoning. Refrigerate for at least 30 minutes before serving.