Preheat the grill to medium heat.
Cut the peaches in half and remove the pits carefully.
Brush the cut side of the peaches lightly with olive oil.
Brush the grill grates with olive oil if needed to prevent sticking.
Place peaches cut side down on the grill and cook for 8 to 10 minutes until grill marks form and peaches soften.
While the peaches cook, melt the butter in a microwave-safe bowl.
Stir sugar and cinnamon into the melted butter mixture.
Remove peaches from the grill and place them on a rimmed baking sheet or serving platter.
Slowly spoon the cinnamon butter mixture over the grilled peaches so it soaks into the centers.
Serve warm with vanilla ice cream and any toppings you prefer.
