Preheat oven to 350°F (175°C) and grease two 8-inch round cake pans.
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 the pumpkin purée and the dissolved espresso mixture until smooth.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Divide batter evenly between the prepared pans and bake for 30 to 35 minutes or until a toothpick comes out clean.
Cool cakes in pans for 10 minutes, then transfer to a wire rack to cool completely.
To make the frosting, beat cream cheese and butter in a bowl until smooth and creamy.
Add powdered sugar, vanilla, and 1 tablespoon espresso powder, then beat until light and fluffy.
Apply a layer of frosting between the two cooled cake layers and cover the top and sides of the cake.