Preheat the oven to 350°F (175°C). Grease and line a 15×10-inch jelly roll pan with parchment paper.
Whisk together flour, baking powder, baking soda, salt, and pumpkin pie spice in a bowl.
In a separate large bowl, whisk pumpkin puree, oil, granulated sugar, brown sugar, eggs, and vanilla until smooth.
Gradually add the dry ingredients to the wet ingredients. Mix just until combined; don't overmix.
Spread the batter evenly into the prepared pan.
Bake for 20–25 minutes, or until the center springs back lightly and a toothpick comes out clean.
Allow the bars to cool completely before frosting.
For the frosting, beat cream cheese and butter until smooth. Gradually add powdered sugar and vanilla, beating until creamy.
Add milk or heavy cream, a little at a time, if needed to reach a smooth spreading consistency.
Spread the frosting over the cooled pumpkin bars.
Chill briefly for cleaner slices, then cut into 24 bars and serve.