Whisk flour, cinnamon, ground ginger, nutmeg, salt, cloves and baking soda together in a medium bowl. Set aside.
Whisk brown sugar, melted butter, molasses and crystallized ginger in separate large bowl until combined. Whisk in egg, buttermilk and vanilla until combined. Add flour mixture and stir with rubber spatula just until dough comes together. Cover bowl with plastic wrap and refrigerate for at least 1 hour up to 24.
Preheat oven to 350 degrees F. Line 2 baking sheets with parchment paper or nonstick mat. Roll dough into balls using 1 scant tablespoon. Space balls evenly on prepared sheets, about 2 inches apart. Bake cookies, 1 sheet at a time, until puffed and just set, 11-13 minutes. Let cookies cool on sheet for 5 minutes then transfer to wire rack to cool completely before frosting.
Using stand mixer fitted with paddle attachment, beat butter and powdered sugar on medium-high speed until fluffy, about 2 minutes. With mixer running, add cream cheese, 1 piece at a time, and continue to beat until smooth, about 30 seconds. Beat in vanilla extract and pinch of salt as needed.
*Spoon or pipe 1 tablespoon frosting evenly onto bottoms (flat sides) of 24 cookies. Top with remaining 24 cookies, bottom sides down. Dust with powdered sugar. (Note, these cookies need the dusting of powdered sugar or they won’t taste sweet enough).
Store cookies in an airtight container in the refrigerator. Bring to room temperature before serving.