In a large bowl, stir together the pumpkin puree, granulated white sugar, brown sugar, and oil.
Then stir in the eggs and vanilla extract. Set aside.
In a medium bowl, whisk together the all-purpose flour, pumpkin pie spice, baking powder, baking soda and salt.
Stir the dry ingredients into the wet ingredients until no dry flour is still visible.
Butter or spray (with nonstick cooking spray) a 9×13 baking pan. Then spoon the batter in an even layer.
Bake at 350°F (177°C) for 26-28 minutes, until a toothpick inserted in the cake comes out clean (no gooey batter on the toothpick).
Allow the cake to fully cool before adding frosting.
To make the frosting, cream together the softened butter and softened cream cheese.
Then incorporate the vanilla extract and powdered sugar (confectioners' sugar). Spread the frosting over the cooled cake.