In a large mixing bowl, combine the pumpkin puree, applesauce, sugar and vanilla.
Add the eggs and stir to combine all ingredients.
Add the flour, baking powder, pumpkin pie spice, baking soda, and salt.
Gently fold in the dry ingredients until mixed and all the flour is absorbed.
Pour the batter into a lightly greased 13x9 baking dish.
Bake for 35 minutes or until a toothpick inserted in the middle comes out clean.
Remove from the oven and place on a cooling rack. Allow to cool for at least one hour before frosting.
Frosting
Add the cream cheese, butter and vanilla to the stand mixer.
Using the paddle attachment, whip on high speed until the mixture is combined, light, and fluffy.
Add the powdered sugar to the mixer.
Turn the paddle on slowly until the powdered sugar begins to mix with the cream cheese and butter.
Increase the speed to whip the frosting until it is combined, light and fluffy.
When the bars are cool enough to frost, spread the frosting over the entire top of the bars. Serve immediately or refrigerate, covered, for up to 1 week.