Stir the flour, baking soda, cream of tartar and salt in a medium bowl.Heat oven to 350ºF.  Beat 1 cup shortening, granulated sugar, brown sugar and 2 tablespoons milk in a large bowl with an electric mixer on medium-high speed until the mixture is light and fluffy.  Add the eggs, one at a time, beating well after each addition.  Beat in 1 teaspoon vanilla extract.Reduce the speed to low.  Add the flour mixture and beat until the mixture is smooth.  Shape the dough into 3 flat disks.  Cover and refrigerate for 1 hour or until firm.Heat the oven to 350ºF.  Place the disks on a lighly floured surface.  Roll each disk to 1/4-inch thick.  Cut the dough using your favorite cookie cutters.  Place the cut-outs onto baking sheets.Bake for 8 minutes or until the edges of the cookies are lightly browned.  Let the cookies cool on the baking sheets on wire racks for 10 minutes.  Remove the cookies from the baking sheets and let cool completely on wire racks.Beat the remaining shortening, vanilla extract and the confectioners' sugar in a medium bowl with an electric mixer on medium speed until the mixture is smooth.  Decorate the cookies with the icing.