Preheat the oven to 350°F. Grease two 6-inch round cake pans and line the bottoms with parchment.
In a large bowl, whisk together the pumpkin puree, granulated sugar, brown sugar, eggs, and vegetable oil until smooth.
In a separate bowl, stir the flour, baking soda, pumpkin pie spice, salt, and black cocoa powder.
Add the dry ingredients to the wet ingredients and mix until just combined. Divide the batter evenly between the prepared pans.
Bake for 22-25 minutes, until a toothpick inserted in the center comes out clean. Cool the layers in the pans for 10 minutes, then turn them out onto a wire rack to cool completely.
Beat the cream cheese and butter together until creamy. Gradually add the powdered sugar and vanilla, then beat until light and spreadable.
Place one cooled cake layer on a plate. Spread a thick layer of frosting on top. Set the second layer over the frosting and cover the top and sides with the remaining frosting.