Preheat oven to 350°F (175°C) and grease a 9x13 inch baking pan.
In a medium bowl, whisk together flour, baking soda, baking powder, salt, cinnamon, ginger, cloves, and nutmeg.
In a large bowl, beat granulated sugar, brown sugar, and vegetable oil until combined.
Add eggs one at a time, beating well after each addition.
Stir in pumpkin purée and vanilla extract.
Gradually add the dry ingredients to the wet ingredients, stirring until just combined.
Pour batter into the prepared pan and bake for 45 to 50 minutes, or until a toothpick inserted into the center comes out clean.
Allow cake to cool completely in the pan on a wire rack.
For the frosting, beat cream cheese and butter until smooth.
Gradually add powdered sugar and orange zest, beating until light and fluffy.
Spread frosting over the cooled cake before serving.