**Preheat Oven:** Preheat your oven to 350°F (175°C) and lightly grease your baking dish.
**Prepare the Filling:** In a large mixing bowl, combine the apple slices, granulated sugar, brown sugar, flour, cinnamon, nutmeg, salt, and vanilla extract. Toss until the apples are evenly coated. Spread the apple mixture evenly into the prepared baking dish. Drizzle caramel sauce over the apples.
**Make the Topping:** In another bowl, whisk together the flour, sugar, baking powder, and salt. Add the milk and melted butter, stirring until a smooth batter forms.
**Assemble the Cobbler:** Pour the batter over the apple mixture, spreading it gently with a spatula to cover most of the apples.
**Bake:** Bake for 40–45 minutes, or until the topping is golden brown and the apples are tender.
**Serve:** Let the cobbler cool slightly before serving. Drizzle additional caramel sauce over the top for extra flavor.