Preheat oven to 350. Whisk together flour, cinnamon, ginger, baking soda and salt. Set aside.
Cream together oil, sugar, molasses and vanilla. Add dry ingredients and mix into a soft dough. Place mixture on parchment paper and roll into a log approximately 9-inches in length. Refrigerate for about 30 minutes until more easy to handle.
Mix together powdered sugar, shortening, vanilla. Add enough water (plus a few drops of coloring if desired) to form a smooth frosting. Frost cooled cookies and add decorations as desired.