With an electric mixer or by hand, cream butter and sugars in a large bowl. Add eggs and vanilla. In a separate large bowl, sift together the flour, cream of tartar, baking soda and salt. Add flour mixture to egg mixture in 3 additions. Stir in nuts.
Divide the dough into quarters, and then roll it into 4 logs. Place dough in refrigerator to chill for 2 hours. Remove dough and cut into 1/4-inch thick slices. Place on a floured, but not greased, baking sheet and bake for about 15 minutes. Remove to a rack and cool.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.