Preheat oven to 350 degrees Fahrenheit.
In the bowl of an electric mixer cream together softened butter, sugar, and egg until fluffy. Add the molasses and mix just until incorporated.
In a separate bowl, whisk together baking soda, salt, cinnamon, cloves, ginger and flour.
Add flour mixture to wet mixture and mix just until incorporated.
Scoop or roll dough into 1 1/2" balls, roll them in sugar, then place them on a nonstick baking mat or greased cookie sheet 2" apart. Bake for 7 to 8 minutes. Don't over bake or they won't be soft!
Let cool slightly, then carefully remove them to a cooling rack. Whisk together powdered sugar and milk (just enough for thinning) and drizzle over cookies. Allow the glaze to set and the cookies to cool completely. Store in an air tight container.