In a bowl attached to a stand mixer, place the eggs, sugars, oil, butter, vanilla and pumpkin. Beat with the paddle attachment ( or with an electric mixer if you don't have a stand mixer) until light and fluffy.
Sift together the flour, baking powder, baking soda, pumpkin pie spice and salt. Add to the pumpkin mixture slowly, with the mixer on low, and mix until thoroughly combined.
Spread the batter evenly into a 9x13 pan. Bake for 25 to 30 minutes in preheated oven. The bars will be done when a toothpick inserted into the middle comes out clean. Don't over bake! Start checking around the 25 minute mark!
Cool the bars completely before frosting.
Cream Cheese Icing
To make the frosting, cream together the cream cheese and butter. Stir in vanilla. Add confectioners' sugar a little at a time, beating until mixture is smooth. Spread evenly on top of the cooled bars. Cut into squares.
If you want less creamy bars, use a 15 ounce can of pumpkin, this will make the bars more of a cake. My family ADORED the super rich taste when I used the 28 ounces of pumpkin, it's all up to your preference!