1. Preheat the grill to medium-high heat.
2. Lightly oil the grill grates to prevent sticking.
3. Brush the cut sides of the peaches or nectarines with a little olive oil.
4. Place the peaches or nectarines cut-side down on the preheated grill for about 2 minutes, or until they have nice grill marks.
5. Remove from the grill immediately and set aside. Cut each half into wedges.
6. Whisk all the dressing ingredients together in a bowl to dissolve the miso and combine with the rest of the vinaigrette ingredients.
7. Season with salt and pepper to taste.
Assemble the salad:
8. Spread the arugula on a serving plate.
9. Spread the burrata randomly. Top with the grilled peaches or nectarines, fresh blueberries, and chopped pistachios.
10. Zest a lemon over the salad and drizzle with the dressing.