In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl with a handheld mixer, stir together the flour, brown sugar, cinnamon, ginger, salt, baking soda, and cloves until combined.
Using a fork, your fingers, or a pastry cutter, cut in cold butter until small pea-sized pieces remain and the mixture resembles the texture of wet sand.
With the mixer on low speed, slowly beat in the molasses and milk. Beat until the dough is evenly moistened. Increase speed to medium and beat thoroughly until well combined. The dough will appear crumbly.
Turn dough onto work surface and shape into a disk. Wrap with plastic wrap and refrigerate for 1-2 hours or overnight.
Once dough is chilled, preheat oven to 350°F. Line two baking sheets with parchment paper and set aside.
Using a 1 tablespoon cookie scoop, scoop dough and roll into balls. Roll each ball in granulated sugar until fully covered followed by powdered sugar until fully covered. Place on baking sheet about 1½ inches apart.
Bake until the centers are set, about 10-12 minutes. Let cookies cool on pans for 2 minutes and then transfer to wire rack to cool completely.
Pipe or spread vanilla bean cream cheese frosting onto the flat side of one cookie. Place the flat side of another cookie on top to make a cookie sandwich. Repeat with remaining cookies.