In a medium mixing bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Add the 1 cup sugar, baking soda, and cream of tartar. Beat until combined, scraping sides of bowl occasionally. Beat in egg and vanilla. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour. Cover and chill in the refrigerator for 1 hour.