1. Combine butter and sugar; beat until smooth and creamy.
2. Combine flour, cream of tartar, salt, and baking soda; gradually add to butter mixture.
3. Add vanilla; beat until smooth and well blended.
4. Gently fold in cornflakes and nuts so as not to crush cereal.
5. Drop by teaspoonfuls onto ungreased cookie sheet.
6. Bake at 300° for 12-15 minutes or until lightly browned.