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1. In a large mixing bowl beat the 1/2 cup shortening and the butter with an electric mixer on medium to high speed for 30 seconds. Add the brown sugar, baking soda, and salt. Beat until combined, scraping sides of bowl occasionally. Beat in egg and vanilla until combined. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour and the 3/4 cup ground nuts. Divide dough in half.
2. On waxed paper, shape each portion of dough into a 10-inch-long log. Lift and smooth the waxed paper to help shape the logs. If desired, roll logs in the 2/3 cup finely chopped nuts. Wrap each log in plastic wrap. Chill about 4 hours or until firm enough to slice.
3. Preheat oven to 375 degrees F. Cut logs into 1/4-inch-thick slices. Place slices 1 inch apart on an ungreased cookie sheet. Bake for 10 to 12 minutes or until edges are firm. Transfer to a wire rack set over waxed paper and let cool.
4. If desired, in a small saucepan combine chocolate pieces and the 1 tablespoon shortening. Heat and stir over low heat until smooth. Cool slightly. Transfer chocolate mixture to a small resealable plastic bag; seal bag. Snip off a tiny piece of one corner of the bag. Drizzle melted chocolate over cookies. Let stand until set.