Preheat an outdoor grill or grill pan. Brush the cut sides of the nectarines with oil and place on the grill, cut-side down. Grill until caramelized. Turn over and grill until almost soft, about 1 to 2 minutes more.
Transfer the nectarines to a platter, cut-side up, and place a dollop of cheese in the center of each. Drizzle with honey and grind fresh pepper, to taste, over the top. Garnish with the mint and serve.