Place a small saucepan over medium heat. Pour in the wine and add the brown sugar. Stir well to combine. Bring to a boil, then reduce the heat to low and gently simmer until the wine is reduced to a glaze, about 20 minutes.
Preheat a grill pan over medium-high heat.
Lightly brush the stone fruit halves Kalamata D.O.P. Greek Extra Virgin Olive Oil and sprinkle with salt and pepper. Place the fruit, cut side down, on the hot grill. Grill for 1 minute on each side to lightly mark, turning with tongs. Remove the grilled fruit to a decorative platter.
Drizzle the grilled fruit with the wine glaze. Lay the pieces of cheese on top. Lightly drizzle the remaining wine glaze over the fruit and cheese. Serve immediately