Preheat oven to 350F and line baking sheet with parchment paper.
In a large bowl, using a hand mixer or stand mixer, beat butter and sugars until creamy. Beat in egg, then molasses and vanilla and set aside.
In a medium sized bowl, whisk together flour, baking soda, ground ginger, cinnamon, nutmeg, cloves, and salt.
Slowly add the dry ingredients to wet ingredients, using mixer to combine. Once dough is combined, fold in crystalized ginger.
Using about 1.5 tbsp dough (I used a 1.5 tbsp cookie scoop), scoop onto baking sheet. Roll each cookie dough ball into extra sugar and coat evenly. Bake for 14-16 minutes. Let cool slightly before moving to wire rack to finish cooling.
While cooling, using a hand mixer or stand mixer, beat together icing ingredients, starting with the butter and sugar. Add in extracts and milk until desired consistency.
Once cookies are completely cooled, pipe cream onto the bottom of one cookie and add another cookie on top to make a sandwich. Repeat until all cookies are filled.