Preheat the oven to 325 degrees F. Spray a 10-cup bundt pan with nonstick spray (use baking spray, if you have it).
In a medium bowl, whisk together the flour, baking powder, salt, baking soda, cinnamon, ginger, allspice and nutmeg.
In a separate bowl, use an electric mixer to combine the granulated sugar, brown sugar and oil at medium speed for 2 minutes or until blended and light. Beat in the eggs, one at a time, and then beat for 3 minutes. Beat in the pumpkin, applesauce and vanilla.
With the mixer on low speed, add the dry ingredients in three additions, beating until blended and smooth. Transfer the batter to the prepared pan and smooth the top.
Bake for 45 to 55 minutes or until a tester inserted into the center comes out clean. Let the cake cool in the pan on the rack for 10 minutes, then carefully invert the cake onto a wire rack to cool completely.