Preheat the oven to 160C (320F). Line the bottoms and sides of two 7-inch (17 cm) cake pans with parchment paper.
In a large bowl, combine the white sugar, brown sugar, oil, melted butter, and vanilla extract. Whisk until smooth and well blended.
Add the eggs, one at a time, whisking until fully incorporated.
Add the pumpkin puree and whisk again until fully combined.
Sift in the flour, baking powder, salt, cinnamon, and nutmeg. Gently fold in the dry ingredients until just combined, being careful not to overmix.
Divide the batter evenly between the two prepared pans. Bake for 30-35 minutes, or until a toothpick inserted in the center comes out clean.
Remove from the oven and let the cakes cool in the pans until they are safe to handle. Then, place each cake layer upside down on a cooling rack to cool completely. If assembling the cake the next day, wrap the cooled cake layers in plastic wrap and refrigerate overnight.