Heat a skillet over medium heat. Sprinkle the peaches with the brown sugar, then add the butter to the skillet. Once melted and sizzling, add the peaches and cook until golden and caramelized, about 3 minutes per side.
To assemble the salad, alternate a peach slice with a slice of fresh mozzarella and a few basil leaves, making a low row or a circle. Sprinkle the salad with the smoked sea salt then drizzle generously with the olive oil and balsamic. Devour.