Preheat grill to medium-high heat. Lightly oil the grates.
Slice peaches in half and remove pits. Brush cut sides with oil.
Grill peaches cut-side down for 3-4 minutes until grill marks appear and peaches are slightly softened.
Arrange arugula on a large serving platter.
Add grilled peaches and spoonfuls of burrata (tear or spoon into chunks).
Tear prosciutto into pieces and scatter over salad.
Drizzle with olive oil and balsamic glaze.
Sprinkle with flaky salt, pepper, and fresh herbs.
Serve immediately with crusty bread.