Preheat the oven to 350°F.
Melt the butter. Slice the butter into pieces and place them evenly across the bottom of a 9×9-inch baking pan. Place the pan in the oven and allow the butter to melt completely.
In a medium bowl, combine the sugar, gluten-free flour, milk, salt, and baking powder. Stir until smooth and no lumps remain.
Carefully remove the pan from the oven once the butter has melted. Pour the batter over the melted butter. Use a spatula to gently spread the batter across the bottom of the pan.
Spoon the peaches and their juice over the top of the batter. Do not stir. The peaches and juice should remain on top of the batter. Pour any remaining juice evenly over the peaches.
Return the pan to the oven and bake for 40 minutes, or until the cobbler is golden and cooked through.
Serve. Remove from the oven and allow it to cool slightly before serving. Serve warm, with vanilla ice cream if desired.