Melt the butter: Add the butter to an 8 x 8-inch baking dish. Set the baking dish in the oven and preheat the oven to 350°F. Once the butter is melted in the oven, remove the baking dish, 4-6 minutes. Set the baking dish aside while preparing the batter.
Meanwhile, prepare the batter: Mix the flour, sugar, baking powder, salt, and cinnamon in a bowl. Whisk to incorporate evenly. Add the milk and vanilla extract and whisk until smooth.
Assemble: Pour the batter into the baking dish with the melted butter. There is no need to stir. Add the sliced peaches directly on top of the batter.
Bake in the preheated oven until the cobbler is golden and set in the middle, 45-55 minutes. Once baked, remove from the oven and cool 15 minutes before serving.
