Preheat a clean grill or grill pan to medium-high.
Stir together the wine and the brown sugar in a small saucepan. Bring to a boil, then gently simmer 25–30 minutes or until the mixture is reduced to about 3 tablespoons and creates a thick glaze.
Lightly brush stone-fruit halves with olive oil; sprinkle with salt and pepper. Grill fruit, cut side down, 1 minute on each side. Transfer to 4 plates.
Drizzle fruit with glaze, and top each serving with 1/4 of the pieces of cheese.