Heat a grill pan on the stovetop (or a standard outdoor grill) over medium-high heat. Place the peach halves face down onto the grill, cooking for about 5 minutes or until nice grill marks are achieved and the peaches are warm and have softened a bit, turning the peaches 90 degrees halfway through cooking.
Meanwhile, heat a small saucepan over medium-low heat. Add the butter, honey, and cinnamon. Cook 1-2 minutes or until melted and smooth. Keep warm until the peaches are ready.
Put grilled peach halves onto serving plates. Top with lightly sweetened whipped cream and drizzle with cinnamon honey butter. Top with mint leaves, if using. Serve promptly.