Preheat your oven to 350°F (175°C).
In a mixing bowl, combine the sliced peaches with ½ cup of granulated sugar. Let this mixture sit for about 10 minutes to allow the juices to release.
In another bowl, whisk together the flour, remaining ½ cup of granulated sugar, baking powder, and salt.
Slowly add the milk, melted butter, and vanilla extract into the flour mixture. Stir until just combined; do not overmix.
Pour the batter into the bottom of the greased 9x13 inch baking dish.
Carefully spoon the peach mixture over the batter, including the juices, but do not stir.
Optionally sprinkle cinnamon over the top for added flavor.
Bake in the preheated oven for 35-40 minutes, or until the top is golden brown and a toothpick inserted in the center comes out clean.
Allow the cobbler to cool slightly before serving.
Serve warm with vanilla ice cream for an extra treat.