Line cookie sheets with nonstick silicone baking mats or lightly spray with nonstick baking spray. Preheat oven to 375 degrees Fahrenheit. In the bowl of an electric mixer, cream together softened butter, brown sugar, granulated sugar, egg, molasses and pumpkin puree. Mixture will not be completely smooth.
In a separate bowl, whisk together baking soda, salt, cinnamon, cloves, ginger and flour. Add the flour mixture to the wet mixture and mix, just until incorporated. Don't over mix.
Scoop dough by the heaping spoonful (use a regular metal spoon) and place at least 2" apart on prepared cookie sheets. Use the back of the spoon to flatten them as best you can. Place the sheet in the oven and bake for approximately 9-11 minutes. Allow them to cool for a few minutes on the pan, then carefully remove them to a cooling rack to cool completely.
After they're completely cool, make the glaze. Whisk together powdered sugar and just enough milk to thin it to a drizzling consistency. Be careful not to thin it too much. Drizzle the cookies with the glaze and allow it to set. Store the cookies in an air tight container.