Preheat oven to 350°F (177°C) and spray a 2 quart (8-inch X 8-inch) baking dish with gluten-free cooking spray.
Combine the peaches, 1/2 cup sugar, ground cinnamon, and 2 tablespoons of water in a medium saucepan and mix well. Bring to a boil and simmer for 10 minutes, stirring occasionally. Remove from heat.
Pour the melted butter into the prepared baking dish.
In a medium bowl, whisk together the gluten-free flour, 1/2 cup sugar, gluten-free baking powder, and salt. Gradually whisk in the milk until the batter is smooth. Pour this batter over the melted butter in the baking dish without stirring.
Carefully spoon the cooked peach mixture evenly over the batter. Do not stir. The batter will rise to the top during baking.
Place the cobbler on the middle rack of the preheated oven. Place a baking pan on the rack below to catch any potential overflow. Bake for 35-40 minutes, or until the topping is golden brown and a toothpick inserted into the center comes out clean.
Allow the cobbler to cool for 5-10 minutes before serving.