Pre-heat oven to 350 degrees. Mix together butter and sugar, then beat in egg. Add molasses, salt, cinnamon and ginger. Gradually add in the flour. Drop table-spoonfuls onto a greased cookie sheet, and bake 7-9 minutes.
icing: Stir sugar and milk together until smooth, then add corn syrup and vanilla. If mixture is too thick, add more corn syrup until it is easily spreadable, but not too thin.