I have been working on a chocolate chip cookie recipe for years. The key to this recipe is the browning of the butter. It gives the cookies a caramel flavor that is out of this world. I have discovered that the cookies don't turn out nearly as good when you double the recipe. These cookies never last long enough to put into an airtight container! My family constantly sneaks cookies when I'm not looking!
Preheat oven to 375 degrees. Line baking sheets with parchment paper. Whisk flour and baking soda together in medium bowl; set aside.
Heat 10 tablespoons butter in 10-inch skillet over medium-high heat until melted, about 2 minutes. Continue cooking, swirling pan constantly until butter is dark golden brown and has nutty aroma, 1 to 3 minutes. Remove skillet from heat and, using heatproof spatula, transfer browned butter to large heatproof bowl. Stir remaining 4 tablespoons butter into hot butter until completely melted.
Add both sugars, salt, and vanilla to bowl with butter and whisk until fully incorporated (I use the whisk attachment on my kitchen aid mixer rather than whisk by hand). Add egg and yolk and whisk until mixture is smooth with no sugar lumps remaining, about 30 sec. Let mixture stand 3 min, then whisk for 30 sec. Repeat process of resting and whisking 2 more times until mixture is thick, smooth, and shiny. Using rubber spatula or wooden spoon, stir in flour mixture until just combined, about 1 min. Stir in chocolate chips and nuts (if using), giving dough final stir to ensure no flour pockets remain.
Use a large cookie scoop (#24) to scoop out dough onto prepared cookie sheets. Arrange 2-inches apart, 8 dough balls per sheet. (Smaller baking sheets can be used, but will require 3 batches).
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 to 14 min, rotating baking sheet halfway through baking. Transfer baking sheet to wire rack; cool cookies completely before serving.