Cream butter in a medium mixing bowl; gradually add powdered sugar, beating until light and fluffy. Add egg, beating well. Stir in flavorings.
Sift together flour, cream of tartar, and soda in a medium mixing bowl. Gradually add to creamed mixture, stirring until well blended. Cover and chill at least 2 hours.
Divide dough in half. Turn half of dough out onto a well floured surface. (Keep remaining dough chilled until ready to use.) Roll to 1/8-inch thickness; cut with a floured 2 1/2-inch round cutter.
Place cookies 1 inch apart on ungreased cookie sheets. Bake at 375° for 7 minutes or until edges are lightly browned. Remove from cookie sheets; sprinkle tops with sugar, and cool on wire racks. Repeat procedure with remaining dough.