In a large bowl, cream butter and sugar until light and fluffy. Add eggs, one at a time, beating well after each addition. Beat in vanilla. Combine the flour, baking soda, cream of tartar and salt; gradually add to the creamed mixture and mix well. Cover and refrigerate for 30 minutes or until easy to handle.
On a lightly floured surface, roll out to 1/4-in. thickness. Cut with 2-1/2-in. cookie cutters dipped in flour. Place 2 in. apart on ungreased baking sheets. Bake at 350° for 8-10 minutes or until lightly browned.
For frosting, in a large bowl, beat the butter, confectioners' sugar, milk and vanilla until smooth. Spread or drizzle over cookies. Decorate with colored frosting and sugar if desired. Yield: about 7 dozen.