In a standing mixer, using a paddle attachment, beat the butter and the sugar until smooth.
Add the pumpkin puree, vanilla and egg. Mix to combine.
Add the flour, baking soda, baking powder, cinnamon, salt, nutmeg, ginger, and cloves. Mix until just combined.
Cover and chill the dough for an hour.
Preheat the oven to 350 degrees and line twoo cookie sheets with parchment paper.
Using a medium/ 2 tablespoon cookie scoop, dollop the dough onto the parchment. Gently press the dough balls, slightly. Then bake for 13-15 minutes. Let rest on the cookie sheet for 1-2 minutes, then using a spatula, gently move the cookies to a cooling rack to finish cooling.
While the cookies cool completely, it's time to make the frosting. In the stand mixer, add the butter and cream cheese. Beat with a paddle attachment until smooth and creamy. On low, slowly incorporate the powdered sugar, about 1/2 cup at a time. Once the sugar has been added, add the heavy cream and the vanilla. Set the mixer to medium-high for 5 minutes.
When the cookies are completely cool, using a slanted spatula, spread the frosting onto the cookies. Sprinkle a bit of cinnamon over top and enjoy!