In a large mixing bowl, beat the butter and shortening with an electric mixer on medium to high speed for 30 seconds. Add the sugar, baking soda, cream of tartar, and salt. Beat until combined. Beat in the egg yolks and vanilla. Beat in as much of the flour as you can with the mixer. Stir in remaining flour.
Shape dough into 1-inch balls. Place 2 inches apart on an ungreased cookie sheet.
Bake cookies in a 300 F oven about 20 minutes or until tops are slightly cracked and sides are set (do not let edges brown). Transfer cookies to a wire rack; cool. Makes about 48 cookies.