In a small bowl, whisk together the olive oil, white balsamic vinegar, lemon juice, honey, kosher salt, and freshly cracked black pepper until well combined and emulsified. Taste and adjust seasoning as needed—I find that a touch more lemon juice can brighten the dressing if your peaches are particularly sweet. Set aside while you prepare the salad components.
Slice the ripe peaches into 1/2-inch thick wedges, working over a large platter or shallow bowl to catch any juices. Halve the cherry tomatoes and thinly slice the red onion. Tear the fresh mozzarella into bite-sized pieces. Stack the basil leaves, roll them tightly, and slice thinly to create a chiffonade. Keep all components separate and ready to assemble.
Arrange the peach slices on a large platter or shallow bowl, overlapping them slightly. Scatter the halved cherry tomatoes and torn mozzarella among the peaches. Sprinkle the red onion slices over the top. Drizzle the vinaigrette from Step 1 evenly across the salad—I prefer to dress it right before serving so the peaches don't become too soft, but if you need to make it ahead, hold back half the dressing and add it just before serving. Finish by scattering the fresh basil chiffonade over the top and drizzling with the balsamic glaze.