Start by brushing the peaches with oil while the grill is warming up. Grill the peach slices over medium heat for a couple of minutes until they start showing grill marks. Flip them and continue to grill until tender but not falling apart.
Plate the grill peach slices, top with a slice of mozzarella and then tear and sprinkle the fresh basil leaves on top.
Finish by drizzling some aged balsamic vinegar (the older the better) over the peaches and if you like, season with a little salt and pepper. I didn't season with S&P but looking back, I think the salt may bring out a little bit more flavor while the pepper adds a contrasting taste.