In a large bowl, cream together butter and brown sugar until smooth. Beat in the eggs one at a time then stir in the vanilla. Sift together the flour, baking soda, cream of tartar and salt; blend into the creamed mixture. Mix in the walnuts. Form dough into long roll about 2 inches in diameter. Wrap in waxed paper and refrigerate overnight.
Preheat oven to 350 degrees F (175 degrees C). Lightly grease cookie sheets or line with parchment paper. Unwrap the roll of dough and using a sharp knife, slice the roll into 1/4 inch coins. Place cookies 2 inches apart onto the prepared cookie sheets.
Bake for 10 to 12 minutes in the preheated oven. Remove from cookie sheets to cool on wire racks.
