Spray a 9- by 5-inch loaf pan with non-stick spray, then set it aside. Preheat the oven to 350°.
Combine the applesauce, sugar, brown sugar, eggs, oil, and vanilla extract in a large bowl. Whisk well to blend.
Add in the flour, baking powder, baking soda, salt, cinnamon, and nutmeg. Stir just enough to combine; do not over mix. Fold in the apples.
Transfer the batter into the prepared pan.
Bake on the center oven rack until a toothpick inserted into the center of the bread comes out clean, about 60 minutes.
Remove the pan from the oven and put it on a cooling rack for about 15 minutes, then remove the loaf from the pan and place it on the rack to finish cooling.
To make the caramel glaze topping: Melt butter in a small bowl. Whisk in caramel ice cream topping. Add in powdered sugar, 1/2 cup at a time, whisking in between. Once it's all added, whisk until smooth. If caramel glaze is too thick to drizzle on the bread, put it in the microwave for 20 seconds.
Pour caramel over the top of the apple bread. Let sit 1 hour, until caramel topping has set. Slice and Enjoy! Store leftovers in an airtight container on the counter, or in the fridge. Freeze bread by wrapping completely in plastic wrap twice, then wrapping with foil. Freeze for up to 2 months.