Preheat oven to 350°F (175°C). Grease and flour a 9x13-inch baking pan.
In a large bowl, whisk together flour, baking powder, baking soda, cinnamon, nutmeg, ginger, cloves, and salt.
In another bowl, beat granulated sugar, brown sugar, and oil until well blended.
Add eggs one at a time, beating well after each addition.
Stir in vanilla and pumpkin puree until smooth.
Gradually stir in dry ingredients just until combined.
Pour batter into prepared pan and spread evenly.
Bake for 35–40 minutes, or until a toothpick comes out clean. Cool completely.
For frosting: beat cream cheese and butter until smooth.
Add powdered sugar and vanilla, beat until fluffy.
Spread frosting evenly over cooled bars. Cut into squares and serve.