Preheat your oven to 350°F (175°C).
Grease a 9x13-inch baking pan and line the bottom with parchment paper.
In a medium bowl, whisk together the gluten-free flour, baking powder, baking soda, salt, cinnamon, nutmeg, ginger, and cloves.
In a large bowl, mix the granulated sugar, brown sugar, and vegetable oil until well combined. Then, add the pumpkin puree, eggs, and vanilla extract. Stir until smooth.
Gradually add the dry ingredients to the wet ingredients and stir gently until just combined.
Pour the batter into the prepared baking pan and spread it evenly. Bake for 25-30 minutes.
While the bars are cooling, beat the softened cream cheese and butter together until creamy. Add the vanilla extract and gradually mix in the powdered sugar. Adjust consistency with milk as needed.
Once the bars are completely cool, frost them with the cream cheese frosting and cut into squares.