Bring a large pot of salted water to a boil. Cook the gluten-free orzo according to package directions. Drain and rinse briefly under cool water. Transfer to a large serving bowl and let cool.
Meanwhile, preheat the oven to 375°F. Line a baking sheet with parchment paper.
Arrange the prosciutto slices in a single layer on the prepared baking sheet. Bake for 8–10 minutes, or until crisp. The prosciutto will continue to crisp slightly as it cools. Transfer the prosciutto to a wire rack or plate and let cool completely. Break into large pieces.
In a small bowl, whisk together the olive oil, lemon juice, Dijon mustard, salt, and pepper until well combined.
Add the peaches, mozzarella pearls, basil, and red onion to the cooled orzo. Add about two-thirds of the crispy prosciutto and gently toss.
Pour the vinaigrette over the salad and toss gently until evenly coated. Transfer to a serving platter or large shallow bowl.
Arrange additional peach wedges on top. Scatter the remaining crispy prosciutto, fresh basil leaves, and a few mozzarella pearls over the salad. Finish with freshly cracked black pepper and serve.