Preheat oven to 350 degrees F. Line a cookie sheet with parchment paper.
In a medium bowl, combine flour, ginger, cloves, salt and baking soda.
In the bowl of a stand mixer fitted with the paddle attachment, beat brown sugar with granulated sugar and butter. Add eggs and molasses. Mix in dry ingredients 1 cup at a time.
Roll cookie dough into tablespoon sized balls and place on the parchment paper. Leave 2-inches between the cookies. Bake for 14 to 16 minutes. Remove the cookie sheet from the oven and transfer the cookies from the parchment to cooling racks.
Once cookies are cooled completely, add icing ingredients to a small bowl and whisk until powdered sugar fully mixed into milk (there should not be any lumps). Spread icing over cookies as desired.
If you prefer thicker icing, consider doubling the icing recipe.