Remove your cream cheese and butter from the refrigerator and set out so it has time to soften. Preheat the oven to 350 degrees F. Lightly grease a 9X13-inch non-stick baking pan with cooking spray and set aside.
In a large bowl, whisk together the eggs, sugar, oil, applesauce, pumpkin and vanilla until well-combined.
In a medium bowl, whisk together the flour, baking powder, cinnamon, salt, baking soda, and pumpkin pie spice.
Add the dry ingredients to the wet ingredients and whisk until the batter is smooth. Don't over-mix the batter or it will be tough when baking.
Spread the batter evenly in the prepared pan and bake for 25-35 minutes until a toothpick inserted in the center comes out clean and the top of the bars is set and springs back lightly to the touch.
Let the bars cool completely in the pan.
In a medium mixing bowl add cream cheese and butter. Use a hand mixer to beat together until smooth and no lumps remain.
Add the powdered sugar and vanilla. Start the hand mixer on low and beat together until just combined. Increase the speed to medium-high and continue mixing until soft, fluffy, and no lumps remain.
Once the bars are completely cooled, spread the frosting on the cooled bars. Cut into squares and serve immediately or refrigerate for up to 1-2 days.