In an 8-ounce screw-top jar, combine the vinegar and olive oil. Screw on the lid and shake well. Refrigerate until well chilled. The dressing can be made ahead and stored in the jar in the refrigerator for up to a week.
Remove the pits from the peaches and cut the fruit into quarters. Brush with the bourbon/butter mixture. place on grill cut side down for about 2 minutes or until grill marks appear. Flip peaches so that each size gets grill marks. Remove from grill and allow to cool. Once cooled, cut into ½-¾" bites. If the skin easily slips off, remove it, otherwise leave it on.
Drain the mozzarella if necessary and pat it dry. Use a sharp knife to cut it into ½" bites, if not using pearls or ciliegini.
Cut the tomatoes in half.
Add the peaches, mozzarella and tomatoes to a serving bowl and toss with the dressing. Mix in the basil and adjust seasoning with salt and pepper.