In a large mixing bowl, beat the butter and the shortening with an electric mixer for 30 seconds. Add the 1/2 cup granulated sugar, powdered sugar, baking soda, cream of tarter, and the salt. Beat until combined.
Beat in egg and vanilla. Beat in as much flour as you can with the mixer. Stir in any remaining flour. Cover and chill dough in the refrigerator for about 3 hours or until it's easy to handle.
Shape the dough into 1-inch balls. Roll balls in additional granulated sugar to coat. Place balls 3 inches apart on an ungreased cookie sheet. Flatten to 2-1/2-inch rounds, using the bottom of a glass dipped in additional granulated sugar to prevent sticking, if you like.
Bake the cookies in a 350 degree F oven for 7 to 9 minutes or until they're lightly browned. Transfer the cookies to a wire rack and let cool. Decorate as you like or leave plain.
Flo uses the pattern on a meat mallet for a waffle impression to the tops of these cookies.