Preheat your oven to 350°F (175°C). Grease the baking dish with a little butter or cooking spray.
In a large bowl, combine the sliced peaches with ½ cup of sugar. If desired, add the cinnamon. Allow the mixture to sit for about 10 minutes to release the juices.
In another bowl, whisk together the flour, baking powder, remaining sugar (½ cup), and salt.
Stir in the milk and melted butter into the flour mixture until just combined, creating a smooth batter.
Pour the batter into the greased baking dish. Do not stir; it will create a base for the cobbler.
Spoon the peach mixture evenly over the batter, ensuring to distribute the peaches evenly and allow the juices to flow over the top.
Bake in the preheated oven for about 40 minutes, or until the cobbler is golden brown and a toothpick inserted into the batter comes out clean.
Remove from the oven and allow it to cool for a few minutes. Serve warm, either plain or with a scoop of vanilla ice cream.