Cake: Preheat the oven to 350°F (175°C). Spray a 9x13-inch (23x33cm) baking pan lightly with baking spray and line with parchment paper. Set aside.
In a large mixing bowl, whisk the flour, baking powder, salt, cinnamon, ginger, nutmeg, allspice, and cloves to combine. Set aside.
In another large mixing bowl, whisk the eggs, oil, brown sugar, white sugar, pumpkin puree, and vanilla to combine. Add the dry ingredients and whisk until thoroughly combined. Transfer the batter to the prepared baking pan and spread evenly. Bake for 30-35 minutes or until a toothpick inserted into the center comes out clean. Cover loosely with aluminum foil after 20-25 minutes if the tops brown too quickly. Remove from the oven, place the pan on a wire rack, and cool to room temperature.
Frosting: In a large mixing bowl, using an electric mixer fitted with a whisk or paddle attachment, beat the butter on medium-high speed until creamy, about 2 minutes. Add the cream cheese and mix until smooth and combined. Sift in the powdered sugar and mix until creamy, about 2 minutes. Add the vanilla and mix to combine.
Remove half of the frosting and transfer it to a medium mixing bowl. Add the cinnamon and maple syrup and mix until creamy and combined, about 1 minute.
Alternately spoon dollops of both frostings on top of the cooled cake and spread all over the cake without mixing the two frostings completely up. Refrigerate for 1 hour that the frosting sets, and it's easier to cut. Serve immediately or store in an airtight container in the refrigerator for up to 4 days or freeze for up to 3 months.