With an electric mixer, mix butter, brown sugar and granulated sugar until well combined. Add egg and vanilla extract to the mixture and continue to mix until well incorporated. Next, stir in 1 cup of pumpkin, until mixture is an even orange color. Set aside.
Now, mix flour, baking soda, ground nutmeg, ground cloves, ground ginger, salt and ground cinnamon until well combined. Pour the dry ingredients into the pumpkin mixture and mix well until dough is nice and smooth.
Lightly grease a cookie sheet. Using a spoon, make dough balls and place them on the cookie sheet with enough space between them so they do not spread into each other. Place them in the preheated oven and bake for 10 minutes.
While the cookies are baking, start on the frosting. To make, add butter, heavy cream and brown sugar to a small saucepan and bring to a boil.
After the frosting mixture begins to boil, remove it from the heat and let cool completely. Sift confectioner’s sugar into the frosting mixture and stir until there are no lumps.
Once the cookies and the frosting are cool, frost each cookie generously.