Line two cookie sheets with parchment paper or silicone mats.
In a medium bowl, whisk flour and baking soda together.
In a skillet, heat 10 Tbsp. butter over medium-high heat until melted. Then continue cooking while you swirl the pan until it is dark golden brown and nutty, about 1 to 3 minutes.
Transfer browned butter to a large heatproof bowl and mix the last 4 Tbsp. butter in until it melts completely.
Add sugars, salt, and vanilla and whisk until well combined.
Add egg and yolk and whisk until mixture is smooth.
Let sit for 3 minutes and then whisk for 30 seconds. Repeat two more times.
Using a rubber spatula, stir flour mixture into butter mixture until just combined.
Stir in chocolate chips and nuts.
Each cookie sheet will have 8 dough balls that are about 3 Tbsp. each (so 16 cookies total). Make sure they are 2 inches apart.
Bake in a preheated 375 degree oven for 10 to 14 minutes, one cookie sheet at a time; rotate halfway through baking and bake until cookies are golden brown. They will still be puffy, but the edges will begin to set and the centers will be soft.
Remove to a wire rack to cool. Store in an airtight container.