Preheat the oven to 350°.
In a mixing bowl, combine the first 5 ingredients; set aside.
In a larger bowl, beat together the oil and sugar for 2-3 minutes (use an electric mixer on medium speed).
Add in the egg and molasses; beat well.
Add in the dry ingredients and mix thoroughly.
Drop by rounded teaspoonfuls onto an ungreased cookie sheet, leaving several inches between for expansion.
Sprinkle lightly w/ sugar.
Bake for 12 minutes; cool cookies on cookie sheet for 5 minutes, then transfer to a wire rack to cool completely.
To make the icing: combine the sugar, shortening, and water in a bowl; beat until smooth and creamy; cover until ready to use.
When the cookies are completely cooled, spread a very thin layer of icing on each cookie; let the icing set before stacking the cookies or they will stick together.