1. Preheat oven to 350°F (175°C).
2. If using fresh peaches, blanch them in boiling water for 30 seconds, then transfer to ice water to peel easily. Slice peaches.
3. In a bowl, mix sliced peaches with 1/2 cup sugar, cinnamon, and cornstarch if using frozen peaches. Set aside.
4. In another bowl, combine flour, remaining 1/2 cup sugar, baking powder, and salt.
5. Stir in milk until batter is smooth.
6. Pour melted butter into a 9×13-inch baking dish, then pour batter over the butter. Do not stir.
7. Spoon peach mixture and juices evenly over the batter.
8. Bake for 38 to 50 minutes until the top is golden brown and the filling is bubbly.
9. Let the cobbler cool slightly to thicken before serving.
10. Serve warm with a scoop of vanilla ice cream or whipped cream if desired.