Preheat 325 degrees F. Spray three 8-inch or four 6-inch round cake pans with cooking spray and line the bottoms with parchment paper rounds and spray again. Set aside.
In the bowl of an electric mixer fitted with the paddle attachment, beat the sugar and eggs together on medium-high speed until light and fluffy, about 5 minutes. Add the oil and vanilla and beat on medium until combined, about 30 seconds. Add the pumpkin filling and mix until combined, about another 30 seconds.
In a medium bowl, whisk together the flour, baking powder, cinnamon, ground ginger, nutmeg, and salt, and with the mixer on the lowest speed, gradually add to the pumpkin/egg mixture.
Evenly distribute batter into the prepared pans, smooth with a small offset palette knife and place in the center of the middle rack of the oven, about 2 inches apart. Bake until a knife or toothpick inserted into the center comes out clean, about 30-35 minutes.
Let pans cool on a wire rack 10 minutes, and then invert cakes onto rack and cool them completely.