Adjust oven rack to middle position and heat oven to 375 degrees F . Line 2 large baking sheets with parchment paper. Whisk flour and baking soda together in medium bowl; set aside.
In a medium skillet or saucepan heat 10 tablespoons butter on medium-high heat, about 2 minutes until melted, swirl the pan around constantly until the melted butter is dark golden brown and has nutty aroma, 1 - 3 minutes.
Turn off heat, and transfer browned butter to large heatproof bowl, using heat proof spatula or spoon, stir remaining 4 tablespoons butter into hot butter until completely melted.
Add the brown sugar, sugar, vanilla, and salt to the bowl of melted butter and whisk until fully combined. Add egg and egg yolk, whisk until mixture is smooth and no sugar lumps remains, about 30 seconds. Let mixture rest for 3 minutes then whisk for another 30 seconds.
Repeat this process (whisk and resting) two more times until you get a thick, shiny and smooth dough.
Stir in flour mixture until just combined, about 1 minute. Stir in chocolate chips and nuts, giving dough final stir making sure no flour pockets remain
Divide dough into 16 portions, each about 2-3 tablespoons and place on baking sheets, 8 dough balls per sheet.
Bake cookies 1 tray at a time until cookies are golden brown and still puffy, and edges have begun to set but centers are still soft, 10-14 minutes, rotating baking sheet halfway through baking. Transfer baking sheet to wire rack; cool cookies completely before serving. Serve with a cold glass of milk if desired