Preheat oven to 350°F and grease a 9x13-inch baking pan.
In a bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, nutmeg, cloves, and ginger.
In another bowl, beat pumpkin puree, granulated sugar, brown sugar, eggs, and vegetable oil until smooth.
Stir in brewed coffee and vanilla extract.
Gradually add dry ingredients to wet ingredients, mixing until just combined.
Pour batter into prepared pan and bake for 30–35 minutes, or until a toothpick inserted comes out clean.
Let cake cool completely.
For frosting, beat cream cheese and butter until smooth.
Add powdered sugar and vanilla extract, and mix until fluffy.
Spread frosting over cooled cake and serve.