Preheat the oven to 350°F (175°C). Grease a 9-inch round cake pan with butter and set aside.
In a large bowl, mix together the melted butter, brown sugar, eggs, vanilla extract and ground cinnamon. Add the flour, baking powder and salt. Mix until just combined.
Stir in the applesauce and diced apples. Fold in the chopped pecans or walnuts, if desired.
Pour the batter into the prepared cake pan and spread evenly.
Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and let cool for 10 minutes before transferring to a cooling rack.
Drizzle with caramel topping and serve.
Interesting Facts
This cake is a great way to use up ripe apples.
Feel free to experiment with different types of apples for different flavors.
You can substitute the caramel topping with a powdered sugar glaze.