In a screw top or dressing jar, combine the vinegar and oil. Shake well, and refrigerate until well chilled. (Dressing can be made ahead and stored in the refrigerator up to 1 week.)
Remove the pits from the peaches and cut them into ½-inch thick slices or wedges.
Drain the mozzarella and pat it dry. Using a knife, cut it into ¼-inch thick slices.
On a serving platter, arrange peaches and mozzarella. Scatter torn basil leaves on top, then drizzle with dressing and finish with salt and pepper. Serve immediately.