Make the Filling:

1. Begin by preheating the oven to 375°F. Cut the butter into several pieces and place them in a 9×13 baking dish. Put the dish in the oven until the butter has melted, which should take about 5 minutes. Remove and set aside.
2. Peel the peaches, then cut them in half, discard the pit, and slice them into pieces approximately ¼-inch thick. Transfer the slices to a large skillet.
3. Sprinkle both the brown and granulated sugars over the peaches, mixing them together. Heat the mixture over medium heat, stirring occasionally, until the sugars have dissolved, which will only take a few minutes. Remove from heat and set aside.

Make the Batter and Assemble:

1. In a large bowl, combine the flour, baking powder, salt, sugar, and cinnamon. Pour in the milk and stir until just combined.
2. Pour the batter into the prepared baking dish, spreading it towards the edges without mixing it with the melted butter.
3. Carefully add the peaches along with any liquid into the dish, spreading them out evenly while leaving some gaps for the cobbler topping to rise through.
4. Bake for approximately 40 to 45 minutes. The cobbler is ready when it turns golden brown and springs back when lightly pressed.