In a mixing bowl, cream butter and confectioners sugar. Add vanilla. Gradually add flour, mix well. With lightly floured hands, shape tablespoons into 2 inch logs (looks similar to lady finger cookies). Place 2 inches apart on unthreaded baking sheet. Bake at 350 degrees for 9-11 minutes or until edges and bottom are lightly browned. Cool for 2-3 minutes before removing to wire rack.

In a microwave safe bowl, melt chocolate chips and shortening; stir until smooth. Drizzle chocolate over half of the cookies (entire cookie). Dip one edge of the remaining cookies into chocolate; then sprinkle with walnuts.