Preheat the oven to 350°F (175°C) and lightly grease a 9x13-inch baking dish.

In a large saucepan, combine sliced peaches, granulated sugar, brown sugar, cornstarch, vanilla extract, cinnamon, and lemon juice.

Cook the peach mixture over medium heat for about 5–7 minutes, stirring frequently, until the peaches release juices and the filling begins to thicken slightly.

Remove the peach filling from the heat and pour it evenly into the prepared baking dish.

In a large mixing bowl, whisk together flour, sugar, baking powder, and salt.

Add melted butter, milk, and vanilla extract, then stir until a smooth batter forms.

Spoon the cobbler batter evenly over the peach filling without fully mixing it in.

Bake for 40–45 minutes, or until the top is golden brown and the peach filling is bubbling around the edges.

Remove the cobbler from the oven and allow it to cool slightly before serving.

Dust lightly with powdered sugar before serving if desired.