Cream butter and gradually add sugar, beating until light and fluffy. Stir in vanilla. Gradually add flour and mix well. Shape dough into 2 1/2 inch x 1/2 inch sticks. Place on ungreased cookie sheets. Flatten 3/4 of each cookie lengthwise with tines of a fork to 1/4 inch thickness. Bake at 350 deg. F. for 12 to 14 minutes. Cool. Combine chocolate chips and shortening in top of a double boiler; bring water to a boil. Reduce heat to low and cook until chocolate melts, stirring occasionally. Remove double boiler from heat, leaving chocolate mixture over hot water. Dip unflattened ends of cookies in warm chocolate to coat both sides; roll tips in chopped nuts. Place cookies on wire racks until chocolate is firm. Arrange cookies between layers of wax paper in an airtight container. Store in cool place.