Mix together butter and sugar until light and fluffy, approximately 2-3 min with an electric mixer. Add a slightly beaten egg and molasses and mix well.
In a separate bowl combine flour, baking soda, salt, cinnamon, and ground ginger, and mix to combine. Add the dry ingredients to the wet ingredients and mix until just combined.
The cookie dough will be thick. Cover the cookie dough and let it chill for 1 hour. Form or scoop balls of dough that are slightly smaller than a golf ball.