Preheat oven to 350 degrees F. Line two large baking sheets with parchment paper or Silpat baking mats. Set aside.
In a medium bowl, whisk together the flour, baking soda, baking powder, cinnamon, nutmeg, ginger, cloves, and salt. Set aside.
Using a stand mixer or hand mixer, beat the butter and sugars together until creamy and smooth, scraping down the sides of the bowl with a spatula, as necessary. Add the pumpkin, egg and vanilla and beat until smooth.
Add the dry ingredients and mix on low until just combined. Don’t over mix.
Use a cookie scoop or spoon to drop the cookie dough by rounded tablespoon onto the prepared baking sheets.
Bake for or 14 to 18 minutes or until edges are firm but cookies are still soft in the center. Cool on baking sheets for 2 to 5 minutes; transfer to wire cooling racks to cool completely.
While the cookies are cooling, make the cream cheese frosting. In the bowl of a stand mixer, combine butter and cream (you can also use an electric hand mixer) and beat until creamy and smooth, about 1 minute.
Add the confectioner’s sugar, vanilla, and salt. Mix on low for 30 seconds and then turn to medium speed and mix until smooth, about 1 minute. Stop and scrape down the sides of the bowl, as necessary. If you want a thicker frosting add an additional ¼ cup to ½ cup of confectioner’s sugar and beat again.
Frost the cooled cookies with cream cheese frosting