Preheat your oven to 375°F. Pour the melted butter into a 9x13-inch baking dish, ensuring it evenly coats the bottom.
In a mixing bowl, whisk together the flour, granulated sugar, baking powder, and salt. Slowly add the milk, whisking until a smooth batter forms.
Pour the batter over the melted butter in the baking dish. Do not stir—this layering is essential for the cobbler's unique texture.
Evenly distribute the sliced peaches over the batter. If desired, sprinkle the peaches with cinnamon and a little extra sugar for added sweetness and flavor.
Bake the cobbler for 35-40 minutes, or until the top is golden brown and the batter has risen around the peaches.
Allow the cobbler to cool slightly before serving.