Preheat the oven to 375 degrees F. Grease a 9×13-inch pan with nonstick cooking spray and set aside.
In a large bowl, combine the apple slices, brown sugar, lemon juice, cornstarch, vanilla, cinnamon, cloves, and nutmeg. Stir until the apples are well coated.
Pour the mixture evenly into the prepared pan and set aside while you make the topping.
Place the butter in a small skillet and melt over medium heat, stirring often, until it foams, smells nutty, and browns. This will take about 5 minutes. Scrape the browned butter into a small bowl and let cool to room temperature. You can put it in the refrigerator for 10 minutes while you prepare the topping.
In a large bowl, whisk together the flour, sugar, baking powder, and salt. Stir in the milk, vanilla, and browned butter. Mix until combined.
Pour the topping over the apples in the pan. Spread with a spatula until apples are mostly covered, it is ok if some are peaking out.
In a small bowl, stir together the turbinado sugar and cinnamon. Sprinkle over the cobbler topping.
Transfer the pan to the oven and bake for 35 to 45 minutes or the filling is bubbling, and the top is golden brown and set.
Remove from the oven and let cool for 10 minutes before serving. Serve warm with vanilla ice cream and salted caramel sauce, if desired.