In a large mixing bowl beat the shortening and butter with an electric mixer on medium to high speed for 30 seconds. Add the granulated sugar, brown sugar, and baking soda. Beat mixture until combined, scraping sides of bowl occasionally.
Beat in the eggs and vanilla until combined. Beat in as much of the flour as you can with the mixer.
Stir in remaining flour. Stir in chocolate pieces and, if desired, nuts.
Drop dough by rounded teaspoons 2 inches apart onto an ungreased cookie sheet.
Bake cookies for 8 to 10 minutes or until edges are lightly browned. Transfer cookies to a wire rack; cool.