Preheat a grill to medium-high.
Place the peaches cut side down onto the grill and cook until lightly charred, 2 to 3 minutes, depending on the grill. Transfer the peaches, cut sides up, to a grill-proof baking dish or baking sheet and drizzle evenly with the 6 tablespoons of honey. Sprinkle with the thyme, then place the dish on the grill and cover the grill. Continue to cook until the peaches are soft, about 5 minutes, again depending on the grill. Remove the baking dish from the grill and divide the peach halves between 6 dessert plates. Divide the mascarpone evenly among the plates and drizzle with additional honey, if desired. Serve immediately.