Add vinegar and brown sugar, if using, to a small saucepan and bring to a boil. Reduce to a very low simmer and cook for 10-15 minutes, until liquid reduces by about half and is slightly syrupy. Remove from heat, pour vinegar in a bowl or glass to pour, and set aside to cool and thicken.
In a large bowl, combine panko, flour, parmesan, salt, pepper and cayenne, mixing thoroughly to combine. In a small bowl, lightly beat the eggs. Take each slice of fresh mozzarella and coat it in the beaten egg, then dredge it through the bread crumb mix, pressing on both sides to adhere. Repeat with the remaining slices.
Heat a large skillet over high heat. Add 1 teaspoon of olive oil and sear both sides of the nectarines for 1 to minutes until just warmed, but still somewhat firm. Alternately you can also grill the nectarines directly on the grill. Keep the nectarines warm.
Add the remaining olive oil to the skillet and when hot, fry coated mozzarella, turning carefully once or twice, until golden and cheese starts to melt but still retains its shape, about 1 minute on each side. Drain on paper towels.
To assemble, place one nectarine to a plate, top with 1 slice of fried mozzarella and then a basil leaf. Repeat the layer one more time and finish with a nectarine. Garish with basil and freshly grated pepper. Drizzle on the balsamic glaze.