Heat a griddle or grill over medium heat. Brush peaches with olive oil or butter.
Mix mascarpone cheese with cream and cinnamon, and reserve.
Place peaches cut side down on a hot griddle or grill and cook for 3-4 minutes on each side until tender and browned, with distinct grill marks. Place the peaches on a serving dish, drizzle with honey and serve with the mascarpone cream.