Mix the Dry Ingredients: In a large bowl, whisk together the flour, brown sugar, cinnamon, ginger, salt, baking soda, and ground cloves.
Cut in the Butter: Add the cold cubed butter to the dry ingredients. Use a pastry cutter or your fingers to work the butter in until the mixture resembles coarse crumbs.
Add Wet Ingredients: Stir in the molasses and milk until a soft dough forms.
Chill: Cover the dough and refrigerate for at least 1 hour, I always do a full 24 hours.
Prep to Bake: Preheat oven to 350°F (177°C). Line baking sheets with parchment paper.
Shape + Roll: Scoop the dough into tablespoon-sized balls. Roll each ball first in granulated sugar, then in powdered sugar.
Bake: Place cookies 2–3 inches apart on prepared baking sheets. Bake for 10–12 minutes, until cookies are puffed and cracked but still soft in the center.
Cool: Allow cookies to cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.
Make the Frosting: Beat the softened butter until creamy. Gradually add powdered sugar and vanilla, mixing until smooth and fluffy.
Assemble: Spread frosting on the flat side of one cookie and sandwich with another.
Notes
Store assembled cookie sandwiches in an airtight container at room temperature or refrigerated. These cookies stay soft and are perfect for holiday cookie boxes.