In a jar with a tight lid, combine all dressing ingredients. Set aside.
On individual plates or a serving platter, spread out the spring mix. Arrange the peaches on top of the greens. Strew procuitto or salami pieces, blueberries, and basil leaves over the salad. Top with the whole burrata or mozzarella pearls. Season the salad with salt and pepper to taste.
When ready to serve, cut the burrata in several pieces, releasing the cream. Evenly drizzle the salad with the dressing. Serve.