Preheat your oven to 350°F (175°C). Line a 12"x17" half-sheet baking pan with parchment paper and lightly spray the sides with cooking spray.

In a large mixing bowl or electric mixer, cream together the softened butter and white sugar until smooth. Add the eggs one at a time, mixing well after each addition.

In a separate bowl, whisk together the flour, baking soda, baking powder, cinnamon, pumpkin pie spice, and salt. Gradually add these dry ingredients to the wet mixture, then blend in the pumpkin purée until combined.

Pour the batter into the prepared pan and spread evenly. Bake for 20-25 minutes, or until a toothpick inserted into the center comes out clean. Allow the bars to cool completely before frosting.

To make the frosting, beat the softened cream cheese, butter, and vanilla extract together until creamy. Gradually add the confectioners' sugar, mixing until smooth. If the frosting is too thick, add milk one tablespoon at a time; if too thin, add more sugar.

Spread the frosting evenly over the cooled pumpkin bars. Slice into squares and serve. Store leftovers in the refrigerator.