In a medium bowl, toss the peeled, cored, and sliced apples with the brown sugar, granulated sugar, ground cinnamon, salt, and lemon juice. Make sure every slice is coated evenly.
In a separate bowl, combine the all-purpose flour, rolled oats, baking powder, and chopped nuts. Pour in the melted butter and stir until the mixture is crumbly but holds together when pressed.
Preheat your oven to 350°F (175°C). Spread the apple mixture evenly in the bottom of your skillet. Then sprinkle the crumble topping generously over the apples.
Place the skillet in the oven and bake for 40–45 minutes until the top is golden brown and crisp, and the apples underneath are bubbling hot.
Remove the skillet from the oven and let it cool for 5 minutes. Then drizzle the caramel sauce evenly over the top while still warm.
Serve warm, ideally with a scoop of vanilla ice cream or a dollop of whipped cream.