Whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, ginger, cloves, and salt in a medium bowl.
In a large bowl, beat the softened butter, granulated sugar, and brown sugar until light and fluffy, about 3-4 minutes.
Beat in the pumpkin puree, egg, and vanilla extract until well combined. The mixture might look slightly curdled – this is normal!
Gradually add the dry ingredients to the wet mixture, stirring just until combined. Be careful not to overmix.
Cover the dough and refrigerate for at least 30 minutes to firm up the butter and allow flavors to meld.
Preheat your oven to 350°F (175°C) and line baking sheets with parchment paper.
Scoop rounded tablespoons of dough onto the prepared sheets, spacing them about 2 inches apart.
Bake for 12-14 minutes until the edges are set but the centers still look slightly soft.
While the cookies cool, beat together the softened cream cheese and butter until smooth and creamy.
Gradually add the powdered sugar, vanilla extract, and a pinch of salt, beating until light and fluffy.
Once the cookies have completely cooled, spread a generous layer of cream cheese frosting on top of each cookie.