Stir the flour, baking soda and salt in a small bowl. Set aside.
Add the butter and both sugars to a large mixing bowl and beat with an electric mixer until smooth.
Beat in the eggs, one at a time, then beat in the vanilla.
Gradually beat in the flour mixture.
Gently stir in the chocolate chips and chopped walnuts.
Drop rounded tablespoons of the cookie dough onto ungreased cookie sheets, 2 inches apart.
Bake for 8-10 minutes or until golden at the edges. Allow the cookies to cool on the cookie sheets for 2 minutes, then gently transfer them to a wire rack to cool completely.
Notes
Don't overbake the cookies - ever so slightly underbaked makes them get the classic chewy texture.If you're using salted butter, you don't need to add any more to the batter. If using unsalted butter, add a pinch of salt to the batter.To soften the butter quickly, try grating it on a cheese grater into a bowl, then let it sit for 5 minutes and it will quickly come up to room temperature.Storage: Store your leftover chocolate chip walnut cookies in an airtight container in a cool place for up to 5 days.Freeze: This cookie dough is freezable! For best results, freeze it in balls and then bake from frozen, adding an extra 2 minutes to the total cooking time.