Preheat the oven to 350°F. Spray an 8x8-inch baking dish with nonstick cooking spray. Set aside.
In a large bowl, stir together butter and sugar until well combined.
Add the eggs and egg yolk, one at a time, mixing well after each addition.
Mix in the vanilla extract.
In a medium bowl, whisk together the flour, cornstarch, baking powder, salt, and apple pie spice.
Gradually add the dry ingredients to the butter mixture, mixing until fully incorporated.
Fold in the diced apples.
Spread the batter evenly into the prepared baking dish.
Bake for 50-55 minutes, or until the edges start to turn golden brown and the center is set.
Let the cake cool completely in the pan before topping with caramel sauce.