Step 1: Prepare the peaches. If using fresh peaches, peel, core, and slice them. If using canned peaches, simply drain the syrup. Add the peaches to a saucepan along with 1/2 cup of the granulated sugar and 1/8 teaspoon of salt. Cook on medium heat for about 5-7 minutes, stirring occasionally, until the sugar dissolves and the peaches release some juices. Remove from heat.
Step 2: Preheat your oven to 350°F (175°C). Slice the butter into small pieces and place them evenly into a 9x13-inch baking dish. Place the dish in the preheating oven for 5 minutes, allowing the butter to fully melt. Once melted, carefully remove the dish from the oven.
Step 3: In a large mixing bowl, combine the all-purpose flour, remaining 1/2 cup granulated sugar, baking powder, and the remaining 1/8 teaspoon of salt. Stir well to combine. Gradually add the milk to the dry ingredients, stirring until just combined and a smooth batter forms. Do not overmix.
Step 4: Pour the batter evenly over the melted butter in the prepared baking dish. Do not stir. Gently spoon the peach mixture (including any juices) over the batter, spreading it out evenly. Again, do not stir. Sprinkle the ground cinnamon generously over the top.
Step 5: Bake in the preheated oven for 38-45 minutes, or until the topping is golden brown, and the peach juices are bubbling around the edges. If the top browns too quickly, you can loosely tent it with aluminum foil for the last 10 minutes.
Step 6: Remove the cobbler from the oven and let it cool slightly for about 10-15 minutes before serving. This allows the juices to thicken slightly. Serve warm with a scoop of vanilla ice cream or whipped cream for an extra indulgent treat.