In a medium bowl, combine flour, salt and baking soda. Set aside.
In a large mixing bowl, beat butter with an electric mixer on medium to high speed for 30 seconds. Add granulated sugar and brown sugar. Beat on medium speed until mixture is light and fluffy, scraping sides of bowl occasionally. Beat in eggs and vanilla until combined. Beat in as much of the flour mixture as you can with the mixer. Stir in any remaining flour mixture with a wooden spoon until combined. Stir in chocolate pieces and walnuts.
Drop dough by rounded teaspoons or by using a small ice cream scoop 2 inches apart onto ungreased cookie sheet. (Or, cover and store dough in the refrigerator until chilled. Shape dough into 1-inch balls and arrange cookie sheets.)
Bake in a 375 degree F oven for 9 to 11 minutes or until edges are light brown. Cool on cookie sheets for 1 minute. Transfer to wire racks and let cool. Makes about 60 cookies.