Combine balsamic vinegar and brown sugar in a small saucepan over medium heat. Bring to a boil, reduce heat to low, and simmer about 15 to 20 minutes or until vinegar is reduced to a glaze; set aside.
Brush fruit with olive oil, and sprinkle with salt and pepper. Grill fruit, in batches, 1 minute on each side.
Transfer to a platter.
Drizzle grilled fruit with half of balsamic glaze. Top fruit with cheese, and drizzle with remaining balsamic glaze.
