Preheat the oven to 375 degrees F.
Place peaches on the bottom of a 9-inch pie plate or 8-inch square pan. (see notes)
In a mixing bowl, combine the flour, 1/2 cup sugar, baking powder, 3 1/2 tablespoons melted butter, and the milk.
Spread or dollop the batter over the peaches, leaving a small gap between the batter and the edge of the pan.
In a small bowl, add the 1/3 cup sugar and 1/2 tablespoon butter. Pour the boiling water over the top and stir to thoroughly combine. Pour this mixture evenly over the batter.
Bake for 40-45 minutes or until the cobbler is golden brown on top. Check after approximately 35 minutes and lightly drape with a piece of foil if the top is sufficiently brown.
Remove from the oven and serve hot or at room temperature with vanilla ice cream or whipped cream, if desired.