Preheat oven to 350 degrees. Spray a standard bundt cake pan with nonstick cooking spray and set aside.
In a large bowl, cream together the pumpkin puree, applesauce, eggs, and 1 teaspoon of pumpkin pie spice until well combined. Add in the spice cake mix and stir until well combined.
Pour the batter into the prepared bundt cake pan and smooth top using a rubber spatula. Carefully place in oven and bake for 28-33 minutes, or until a toothpick inserted in the cake comes out clean. Remove from oven and let cool in pan for 10 minutes before flipping over and letting cool on wire baking rack completely.
Cream Cheese Frosting
To make the frosting, place the softened butter and cream cheese in a large bowl and use a handheld mixer to cream together until well combined, about two minutes. Add in the powdered sugar, milk, and pumpkin pie spice and continue mixing, starting on the lowest speed and increasing as the sugar combines with the other ingredients.
Spread the frosting over the top of the cooled cake.
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Notes
Be sure you are using pumpkin puree, rather than pumpkin pie filling. It will say 100 percent pure pumpkin on the label.
Pumpkin Pie Spice is a combination of cinnamon, nutmeg, ginger, cloves, and allspice. If you don't have pumpkin pie spice, you can make your own or just use cinnamon.
Apple sauce keeps the cake moist and replaces the oil and fat in this cake.
When making the cream cheese frosting, be sure you are using room temperature butter and cream cheese. And, don't add the frosting to the cake until it is completely cooled.
Make the cake in advance and store in an airtight container in the refrigerator for up to a week.