Make the peach reduction: Combine balsamic and honey in a small saucepan; bring to a boil over high heat. Reduce to a simmer and cook until reduced by about 1 third and syrupy, about 10 minutes. Remove from heat; set aside.
Heat grill or grill pan to medium-high heat. If using grill pan, brush lightly with olive oil.
Split peaches in half lengthwise, discarding the pit. Grill flesh-side down for 3 to 5 minutes or until grill marks appear and the fruit softens slightly. Remove from heat and transfer to a plate.
Place peaches grilled side up on serving plates. Top each half with a dollop of cheese. Drizzle with balsamic reduction and garnish with mint.