In a mixing bowl, cream butter and sugar. Add eggs, one at a time, beating well after each addition. Beat in vanilla. Combine the flour, cream of tartar and baking soda; gradually add to creamed mixture. Cover and refrigerate for 3 hours or until easy to handle.
On a lightly floured surface, roll out dough to 1/8-in. thickness. Cut with a football-shaped cookie cutter. Place 2 in. apart on ungreased baking sheets. Bake a 350° for 8-10 minutes or until lightly browned. Remove to wire racks to cool.
In a mixing bowl, combine confectioners’ sugar and enough hot water to achieve spreading consistency; beat until smooth. Place 3 tablespoons glaze in a small bowl; set aside. Add cocoa to remaining glaze; stir until smooth. Spread brown glaze over cookies. Pipe white glaze onto cookies to form football laces. Yield: 41/2 dozen.