Preheat the oven to 350°F. Grease a 9 x 13-inch baking dish or spray with nonstick cooking spray. If you'd like to be able to lift the cake out of the pan for easy frosting and slicing later, line with a parchment paper overhang. Set aside.
Beat cake mix, dry pudding mix, pumpkin, oil, water, eggs, 1 ½ teaspoons of the cinnamon, cloves, nutmeg, and ginger in a large bowl with an electric mixer on low speed just until moistened, scraping the side of the bowl frequently. Beat on medium speed for 2 minutes, or until well blended.
Pour the batter into the prepared baking dish. Bake for 30-35 minutes, or until a toothpick inserted in the center comes out clean.
Cool in the pan on a wire rack, and then transfer to a serving platter once it's completely cool, if you'd like.
Once the cake is completely cool, prepare the frosting. Stir the remaining ½ teaspoon of cinnamon into the cream cheese frosting.
Spread the frosting evenly over the cooled cake.
Slice and serve!