In the bowl of a stand mixer (or hand mixer), cream the butter and sugars together for 2 minutes until light and creamy, scraping down bowl as needed. Beat in egg, vanilla, and molasses.
In a medium bowl, whisk together flour, baking soda, salt, cinnamon, cloves, and oats.
Slowly add dry ingredients to wet ingredients and mix until combined. Using a cookie scoop, scoop out dough onto cookie sheet, making sure there’s plenty of room in between (I put 8 cookies on 1 sheet).
Bake for 10-12 minutes until edges are slightly browned. Cool on sheet for 5 minutes before transferring to wire rack to cool completely.
Beat butter on high until creamy, about 2 minutes. On medium speed, add confectioners’ sugar and beat for 2 more minutes. Pour in heavy cream and vanilla extract and beat on high for 2-3 minutes until light and fluffy. Put filling in piping bag (or scoop out with spoon) onto the flat side of a cookie. Place another cookie on top, twisting slightly to adhere.
Store in airtight container at room temperature for 2 days, then in the fridge after that.