Preheat oven to 350 degrees.
Sift together flour, baking powder, baking soda, pumpkin pie spice and salt. Set aside.
Using an electric mixer, beat eggs on medium speed until frothy, 3-4 minutes.
Turn mixer speed to low and slowly add sugars. Beat until very thick.
At a medium speed, mix in pumpkin purée and oil, mixing until thoroughly incorporated.
With the mixer on low, add dry ingredients to the wet 1/2 cup at a time. Do this slowly so that the batter doesn’t develop clumps.
Transfer batter to a 12-14 cup bundt pan that has been coated with a baker’s cooking spray that includes flour (or greased and floured). (Alternatively, you can use the batter to make 24 cupcakes, 2 cake rounds or one loaf cake.)
Bake cake until an inserted toothpick or cake tester comes out clean--about 40 minutes. (Cupcakes will cook in less than half the time.)
Invert cake onto a cooling rack or serving plate. If cake resists, cool in the pan for 15 minutes before inverting. (If cake still resists, cool an additional 15 minutes in the pan.) Cool completely before frosting, at least 1 hour.
Serve plain or top with cream cheese frosting or a vanilla or cinnamon glaze.