Preheat oven to 375F.
In a large bowl, whisk together the flour, salt, and baking soda and set aside. I do not typically recommend using a stand mixer for this recipe as you can easily overmix which can change the texture of your cookies.
Cook 1 stick of butter in large saucepan over medium heat stirring often and scraping the bottom of the pan until the melted butter browns, about 4 minutes. Transfer to a large heatproof bowl.
Cut the remaining stick of butter into pieces and add to the browned butter (it should melt, but not sizzle). Once the butter is melted, add in the sugars and whisk until no lumps remain and then add in the eggs and egg yolks. Add the vanilla then fold in the dry ingredients into the butter mixture (wet ingredients).. Add the white chocolate chips, dark chocolate chips, and chopped walnuts and fold together.
Refrigerate the mixture for 1 hour. Using a spoon or ice cream scoop, portion out 24 balls of dough of about the size of a golf ball and place on rimmed baking sheets. If you refrigerate the cookies dough overnight, let your cookie dough sit at room temperature for 10 minutes before rolling into dough balls. For easy clean up, line your baking sheet with parchment paper.
Bake the cookies and rotate if necessary. Allow the cookies to bake at 375F until deep golden brown, about 8-10 minutes. Allow to cool on the baking sheets and then serve.