Preheat your oven to 350°F (175°C). Grease a 10×15-inch jelly roll pan or a standard 9×13-inch baking dish with butter or non-stick cooking spray to ensure the bars release easily after baking.
In a large mixing bowl, whisk together the pumpkin puree, eggs, vegetable oil, granulated sugar, and vanilla extract. Whisk until the mixture is smooth and the sugar is well incorporated.
In a separate medium bowl, sift or whisk together the all-purpose flour, baking powder, baking soda, ground cinnamon, pumpkin pie spice, and salt. This ensures there are no lumps and the spices are evenly distributed.
Gradually add the dry ingredients to the pumpkin mixture. Stir gently with a spatula or whisk until just combined. Be careful not to overmix, as this can make the bars less chewy and more tough.
Spread the batter evenly into your prepared baking pan. Bake for 25 to 30 minutes, or until a toothpick inserted into the center comes out clean. Remove from the oven and let the bars cool completely in the pan on a wire rack.
While the bars cool, beat the softened cream cheese and butter together in a bowl until smooth and creamy. Add the powdered sugar, vanilla extract, and a splash of milk. Beat on low speed until combined, then increase to high until the frosting is light and fluffy.
Once the bars are completely cool, spread the cream cheese frosting evenly over the top. Cut into squares and serve. If the bars are still warm, the frosting will glass melt, so patience is key!