Whisk together the vinegar, mustard, salt and pepper in a small bowl. While whisking, slowly drizzle in the ⅓ cup olive oil and whisk until dressing is emulsified.

Heat 1 Tbsp. olive oil in a large skillet over medium-high heat. Once hot, add prosciutto and cook, turning every 2-3 minutes until crispy. Remove to a plate but leave all the brown bits behind in the pan. If there’s no oil remaining in the pan, add another tablespoon of olive oil and once hot, add peach quarters and cook until just browned, about 2 minutes per side. Remove from heat.

Toss the arugula with ¼ cup of the dressing and place on serving plate. Place burrata on the center of greens and arrange peach slices and prosciutto around the cheese. Drizzle another tablespoon of dressing over the burrata.  Serve additional dressing on the side. Right before serving, open burrata ball and allow some of the creamy center to ooze out onto the salad.