Preheat the oven to 375°F. Spray a 10×15-inch jelly roll pan with cooking spray.
In a large bowl, whisk together the gluten-free flour, baking soda, baking powder, salt, cinnamon, cloves, ginger and nutmeg.
In a small bowl or large measuring cup, combine the pumpkin, milk and vanilla extract, then whisk together until smooth.
Add the eggs, granulated sugar and brown sugar to the bowl of a stand or hand mixer. Mix on medium-high speed for 2-3 minutes, until fluffy and pale in color. With the mixer running on low, slowly drizzle in the oil. Mix until combined.
With the mixer running on low, add ½ of the dry ingredients. Mix until combined, then add ½ of the pumpkin mixture. Repeat with the rest of the dry ingredients and pumpkin mixture, mixing well after each addition. Scrape the bottom of the bowl to make sure everything is well-combined.
Pour the batter into the prepared pan and spread into an even layer.
Bake for 25-30 minutes, or until a toothpick inserted into the center of the bars comes out clean. Cool completely before frosting.
FOR THE CREAM CHEESE FROSTING: In the bowl of a stand mixer, or using a hand mixer, beat the cream cheese and butter on medium high speed until creamy, about 2 minutes. Add the powdered sugar and vanilla and mix on low speed for 30 seconds, then increase to medium-high speed and whip for 2 minutes.
Frost the pumpkin bars. Chill for 1 hour before slicing. Store leftover pumpkin bars in the refrigerator.