Preheat the oven to 350 degrees F. Line two large cookie sheets with parchment paper or silicone mats.
Cookies: Combine the flour, baking powder, baking soda, salt, cornstarch, cinnamon, nutmeg, ginger, and cloves in a medium bowl and whisk. Set aside.
In a large bowl, add the sugar, brown sugar, and butter. Using an electric hand mixer at medium speed, beat the sugars and butter together until combined and fluffy.
Add one of the eggs, and beat until just mixed. Add the second egg and vanilla extract, and continue beating until mixed. Add the pumpkin puree, and beat until smooth.
Pour the dry ingredients into the wet ingredients, and stir together with a wooden spoon or spatula until just mixed. (Lumps in the batter are okay.) The batter will be thick and sticky.
With a cookie scoop (I used a 1 1/2 tablespoon scoop), drop the cookie dough onto the cookie sheets about 2 inches apart. (I could fit 12 cookies onto 1 piece of parchment paper.) Bake the cookies, one cookie sheet at a time, in the preheated oven for 13-15 minutes or until the cookies have risen and the edges are golden brown. Set aside to cool while you make the cream cheese frosting.
Cream cheese frosting
Add the cream cheese, butter, powdered sugar, and heavy whipping cream to a large or medium bowl, and cream together with an electric hand mixer until well-mixed and smooth.
Use a small spatula or spoon to spread the cream cheese frosting on top of the cooled cookies. Dust with extra cinnamon, if desired, and serve at room temperature.
Notes
Use 1 tablespoon of Pumpkin Pie Spice instead of the cinnamon, nutmeg, ginger, and cloves. I prefer using individual spices because the flavors are more potent.
Store these cookies in an airtight container in the refrigerator.