1Preheat the oven to 375 degrees and place the oven rack in the middle position. Line large (18×12 inch) baking sheets with parchment paper and set aside.
Whisk flour and baking soda together in medium bowl and set aside.
2Heat 20 tablespoons of the butter in 10-inch skillet (if possible, do not use nonstick) 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 8 tablespoons butter into hot butter until completely melted.
Add both sugars, salt, and vanilla to bowl with butter and whisk until fully incorporated. Add egg and yolk and whisk until mixture is smooth with no sugar lumps remaining, about 30 seconds. Let mixture stand 3 minutes, then whisk for 30 seconds. 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 minute. Stir in chocolate chips and nuts (if using), giving dough final stir to ensure no flour pockets remain.
3Scoop dough by Tablespoonsful. Arrange 2 inches apart on prepared baking sheets, about 12 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, around 9-10 minutes, rotating
baking sheet halfway through baking.
Transfer baking sheet to wire rack; cool cookies completely before serving.
*I use whatever I have on hand and sometimes I use 2 or 3 kinds together...milk, semi, dark.