01 - Preheat a grill or grill pan to medium-high heat.
02 - Lightly brush peach halves with a bit of olive oil. Grill cut side down for 2-3 minutes per side until grill marks appear and peaches are slightly softened. Remove and let cool slightly, then slice each half into wedges.
03 - In a small bowl, whisk together olive oil, balsamic glaze, honey, Dijon mustard, salt, and pepper to make the dressing.
04 - In a large salad bowl, toss arugula with half the dressing. Arrange on a serving platter.
05 - Distribute grilled peach slices and red onion over the arugula. Tear burrata into chunks and arrange on top. Sprinkle with fresh basil leaves and nuts, if using.
06 - Drizzle the remaining dressing and extra balsamic glaze over the salad. Serve immediately.