Preheat oven to 350 degrees F. Line two large baking sheets with parchment paper and set aside.
In a medium bowl, combine the flour, ginger, cinnamon, cloves, nutmeg, baking soda and salt. Mix well and set aside.
In a large mixing bowl, combine the brown sugar, butter, egg and vanilla. Mix until creamy. Add the molasses and milk and stir until incorporated. Gradually add flour mixture and again stir until incorporated.
Dust a flat surface with flour and roll out the dough with a rolling pin to 1/4-inch thickness. Use cookie cutters to cut shapes into the dough. Place onto prepared baking sheets and bake in the preheated oven for 8-9 minutes. Let cool. (If you need to refrigerate dough, let it reach room temperature before rolling it out.)
Make icing: Combine the powdered sugar and milk in a medium bowl and mix until smooth and creamy. Spoon into ziploc bags and cut 1/8 of an inch off one of the corners. Squeeze icing onto cooled cookies into decorative patterns, as desired.