1. Preheat oven to 350 degrees.  Line a baking sheet with parchment paper and set aside. 
2. In the bowl of an electric mixer with the paddle attachment, cream butter and sugar together on medium speed until pale yellow. Add egg and molasses and mix. 
3. In a separate bowl, mix flour, baking soda, ginger, cinnamon, cloves, and salt.  On low speed, add the flour mixture to the wet ingredients and mix until a dough forms.  Scrape down the edges of the bowl and mix on low speed again until everything is combined well.  
4. Shape the dough into balls with 1/4 cup dough each and roll in granulated sugar.  Cook six dough balls per cookie sheet for 15-16 minutes.  

For the Frosting

1. In the bowl of an electric mixer with the whisk attachment, whisk butter, brown sugar, and powdered sugar on medium speed until smooth, stopping to scrap down the sides as you go.  Add vanilla extract.  Slowly add heavy cream and mix on medium- high speed until light and fluffy (about 1 minute).  Spread onto cooled cookies.