Preheat oven to 350 degrees F (175 degrees C). Lightly grease a jelly roll pan.
Beat pumpkin, white sugar, vegetable oil, and eggs together in a large mixing bowl. Combine flour, baking powder, cinnamon, pumpkin pie spice, baking soda, and salt in a sifter; sift into the pumpkin mixture and mix well; pour into the prepared pan.
Bake in preheated oven until center springs back when lightly touched, 35 to 40 minutes. Cool completely before frosting.
Beat cream cheese and butter together in a bowl until smooth; add vanilla extract and beat. Gradually beat confectioners' sugar into the frosting, adding in small amounts and assuring each batch is incorporated before introducing the next. Spread over the pumpkin bars.