Slice tomatoes into 1 cm rounds or wedges. Season lightly with flaky salt. Set aside 5 minutes to begin releasing juice.
Halve peaches, remove pits, and slice each half into 4–5 wedges. Do not peel.
Slice red onion paper thin. Soak in cold water 5 minutes. Drain thoroughly.
Whisk olive oil, balsamic, honey, and mustard together until emulsified. Season with salt and pepper.
Arrange alternating tomato slices and peach wedges across a large flat platter in a loose, overlapping pattern.
Scatter drained red onion over the top. Tuck torn mozzarella or burrata between the slices if using.
Drizzle all the dressing evenly over the platter.
Scatter torn basil leaves over the top. Season with extra flaky salt and cracked black pepper.
Rest for 10 minutes before serving. Spoon the accumulated juices back over the salad.
Finish with extra basil, a final drizzle of olive oil, and pine nuts or pistachios if using. Serve immediately at room temperature.