In a medium bowl stir together flour, ginger, baking soda, cinnamon, salt, nutmeg, and cloves; set aside.
In a large mixing bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Add brown sugar and molasses. Beat until combined, scraping sides of bowl occasionally. Beat in egg until combined. Gradually beat in flour mixture until combined. Cover and chill dough about 1 hour or until easy to handle.
Preheat oven to 325°F. Line two cookie sheets with parchment paper. Roll 1/3-cup portions of dough into balls. Place four or five balls 4 inches apart on each cookie sheet. Flatten balls slightly.
Bake for 15 to 18 minutes or until edges of cookies are set. Do not overbake. Cool on cookie sheets for 10 minutes. Transfer cookies to a wire rack and cool completely. Spread cookies with Powdered Sugar Icing. Let stand until icing is set.
In a small bowl stir together powdered sugar, vanilla, and 1 tablespoon milk. Stir in additional milk, 1 teaspoon at a time, until icing reaches spreading consistency.