Preheat the oven to 350°F and lightly coat a 9x13-inch baking dish with cooking spray.
In a large mixing bowl, whisk together the eggs, sugar, oil, pumpkin puree, and vanilla extract until well blended.
In a separate bowl, combine the flour, baking powder, cinnamon, pumpkin pie spice, salt, and baking soda, whisking until evenly mixed.
Gradually fold the dry ingredients into the wet mixture, stirring until just combined without over-mixing.
Pour the batter into the prepared baking dish and spread it evenly.
Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
Remove from the oven and let the bars cool in the pan on a wire rack until they reach room temperature.
For the frosting, mix the softened cream cheese, butter, and vanilla extract in a bowl until smooth.
Gradually add powdered sugar, stirring until the frosting reaches the desired consistency.
Evenly spread the frosting over the cooled bars,
Slice into squares, and enjoy!