Beat brown sugar, shortening, egg, and vanilla in a large bowl with electric mixer at medium speed until fluffy. Stir in pecans and cherries.
Sift together flour, baking soda, cream of tartar, and salt in medium bowl, add by 1/2 cupsful to shorteding mixture, beating well after each addition.
Divide dough in half. Place on sheet of waxed paper, shape into a log. refrigerate until firm.
Preheat oven to 400 degrees, cut dough into 1/8" thick slices. Place on a ungreased cookie sheet. Bake 6-8 minutes or until golden brown . Cool 1-2 minutes on cookie sheet . Remove to wire rack , cool completely.