**Preheat the Oven:** Preheat your oven to 350°F (175°C).
**Prepare the Batter:** In a mixing bowl, whisk together the self-rising flour, sugar, and milk until smooth.
**Assemble the Cobbler:** Pour the melted butter into a 9x13-inch baking dish. Pour the batter over the butter—do not stir. Evenly spread the peach slices on top of the batter. If desired, drizzle vanilla extract over the peaches and sprinkle with cinnamon.
**Bake:** Bake for 40-45 minutes, or until the top is golden brown and the edges are bubbling.
**Cool and Serve:** Let the cobbler cool slightly before serving. Enjoy warm with a scoop of ice cream or whipped cream!