Preheat your grill to medium-high heat or prepare a campfire with a grill grate.
In a small bowl, mix the melted butter with 1 tablespoon of honey.
Brush the cut sides of the peaches with the honey-butter mixture.
Place the peaches cut-side down on the grill or grill grate.
Grill for 3-4 minutes, or until grill marks appear and the peaches are slightly softened.
Flip the peaches and grill for an additional 2-3 minutes on the skin side.
While the peaches are grilling, mix the Greek yogurt with the remaining 1 tablespoon of honey and the cinnamon.
Remove the peaches from the grill and let cool for a minute.
Serve the grilled peaches warm, topped with a dollop of the honey-cinnamon yogurt.
Drizzle with extra honey and garnish with fresh mint leaves if desired.