In a large bowl, beat the confectioners' sugar with butter until smooth. Stir in the egg and vanilla. Combine the flour, baking soda and cream of tartar; mix into the batter until well blended. Cover and refrigerate dough for 2 to 3 hours.
Preheat oven to 375 degrees F. Divide dough in half and roll 3/16 inch thick on floured surface. Cut dough with cookie cutters and sprinkle with white sugar. Place cookies onto greased baking sheets.
Bake for 7 to 8 minutes in the preheated oven, or until delicately golden.