In a large mixing bowl, beat butter and shortening with an electric mixer on medium to high speed for 30 seconds.
Add the brown sugar, granulated sugar, baking soda and salt. Beat until the mixture is combined, scraping the sides of the bowl often. Beat in eggs and vanilla until combined. Beat in as much of the flour as you can with the mixer. Stir in the remaining flour by hand.
Stir in the chocolate pieces and nuts.
Drop dough by rounded teaspoons 2 inches apart onto an ungreased cookie sheet. Bake for 8-9 minutes or until the edges are light brown. Transfer to a wire rack to cool.