I always start by preheating my oven to 350°F and greasing a 9×13-inch pan with butter or nonstick spray. This step matters more than people think, since a properly greased pan is what keeps your bars from tearing apart when you try to lift them out later. I like lining mine with parchment paper too, leaving an overhang on the sides for easy removal.
In my largest mixing bowl, I whisk together the eggs, sugar, pumpkin puree, oil, and vanilla extract until the mixture looks smooth and well combined. There's no need for a mixer here, just a sturdy whisk and a couple of minutes of arm strength. I make sure there are no streaks of egg left before moving on to the next step.
In a separate bowl, I whisk together the flour, baking powder, baking soda, cinnamon, pumpkin pie spice, and salt. Mixing the dry ingredients separately first ensures the leavening agents and spices get evenly distributed, so you won't end up with a bitter bite of baking soda in one corner of the pan.
I gently fold the dry mixture into the wet pumpkin mixture using a rubber spatula, stirring just until no flour streaks remain. Overmixing at this stage is the number one thing that can make your bars turn out tough instead of tender, so I really try to stop as soon as it's combined.
I pour the batter into my prepared pan and spread it into an even layer, then bake for 25 to 30 minutes. I know the bars are done when a toothpick inserted in the center comes out clean or with just a few moist crumbs attached, not wet batter.
This is the step I always want to skip, but never do. I let the bars cool completely in the pan on a wire rack, which usually takes about an hour. Frosting warm bars is a guaranteed way to end up with a melted, runny mess instead of a beautiful frosted top.
While the bars cool, I beat the softened cream cheese and butter together until light and fluffy, about 2 minutes. Then I mix in the vanilla extract and gradually add the powdered sugar, beating until the frosting is smooth, thick, and easy to spread.
Once the bars are fully cooled, I spread the cream cheese frosting evenly over the top using an offset spatula. I like chilling the pan for 20 minutes before slicing, since it makes for much cleaner cuts and a firmer frosting layer.