Brush halved peaches lightly with olive oil.
Grill peaches cut-side down over medium-high heat for 2–3 minutes until grill marks appear. Flip and grill another 1 minute. Let cool slightly and slice.
In a small bowl, whisk together olive oil, honey, lemon juice, salt, and black pepper to make the dressing.
Spread greens on a platter. Arrange grilled peach slices over the greens.
Tear burrata and scatter over the salad. Drizzle with dressing and sprinkle toasted nuts on top.
Serve immediately while peaches are still slightly warm and burrata is creamy.