Cream shortening (or butter) and sugar together. Beat in eggs.
In separate bowl, whisk together flour, salt, baking powder and baking soda. .
Alternate adding milk and flour mixture, then add orange juice and orange zest.
Drop by spoonfuls on cookie sheet lined with parchment paper. Bake for 10-12 minutes. Cookies will be lightly browned on edges. Remove to wire rack to cool completely
Icing
Cream together softened butter, powdered sugar, orange juice and orange zest. Spread over cooled cookies or dip the top of cookies into the icing.