Preheat the grill to medium heat.
In a mixing bowl, combine the 1/4 cup melted butter, brown sugar, and cinnamon. Mix well.
Brush the cut side of each peach half with the butter mixture.
Place the peaches on the grill, cut-side down. Grill for 3-4 minutes, or until they have nice grill marks.
While the peaches are grilling, prepare the crumble by combining the flour, white sugar, baking powder, and salt in a mixing bowl.
Cut in the 1/2 cup chilled butter using a fork or pastry cutter until the mixture resembles coarse crumbs.
Transfer the grilled peaches to a 9-inch square baking dish.
Sprinkle the crumble mixture over the top of the peaches.
Place the baking dish on the grill and close the lid. Grill for 15-20 minutes, or until the topping is golden brown and the peaches are soft and bubbly.
Serve the Grilled Peach Cobbler warm, topped with vanilla ice cream if desired.