Preheat your oven to 350 degrees Fahrenheit.
Toast walnut pieces on a baking sheet for eight minutes until fragrant, then let cool.
Brown the butter in a heavy-bottomed skillet until it reaches an amber color, then remove from heat and cool.
In a medium bowl, whisk together the flour and baking soda.
In a large mixing bowl, combine the cooled browned butter with both brown and white sugars until smooth.
Beat in the eggs and vanilla extract until the mixture is fully emulsified.
Slowly fold the dry flour mixture into the wet ingredients until just combined, being careful not to overwork the dough.
Gently stir in the chocolate chips and toasted walnuts by hand.
Scoop portions of dough onto a lined baking sheet.
Bake for 12 minutes or until the edges are golden brown and the centers remain slightly soft.