Preheat oven to 350 degrees. Place one stick of butter in a small saucepan. Heat over medium heat, allowing butter to melt.
Continue to stir until butter just browns, approximately 7 minutes. Remove from heat and allow to cool.
Cream remaining stick of butter with sugars.
Scrap browned butter into bowl, getting all the browned bits. Mix well.
Add eggs and vanilla. Mix.
Combine flour, salt, and baking soda.
Stir into wet ingredients, until just mixed. Fold in chocolate chips and walnuts.
Refrigerate for 15-30 minutes, allowing the dough to firm up a bit.
Drop cookies by the tablespoon onto an ungreased cookie sheet.
Bake 9-12 minutes, until the edges are crisp. And boom, the perfect chocolate chip cookies.