Preheat your oven to 350°F (180°C) and lightly grease a 9×13-inch baking dish.
In a large bowl, combine the peaches, sugar, lemon juice, cinnamon, and cornstarch. Toss until the peaches are evenly coated.
In another bowl, whisk together the flour, sugar, baking powder, and salt. Stir in the milk and vanilla extract until just combined.
Pour the melted butter into the prepared baking dish, then pour the batter over the butter. Do not stir.
Spoon the peach mixture evenly over the batter without mixing. As it bakes, the batter will rise around the peaches to create the cobbler topping.
Bake for 40–45 minutes, or until the top is golden brown and the peach filling is bubbling around the edges.
Let the cobbler cool for 10–15 minutes before serving. Enjoy warm on its own or with a scoop of vanilla ice cream.