Adjust oven rack to middle position and heat oven to 375 degrees. Line 2 large (18- by 12-inch) baking sheets with parchment paper.
Whisk together 1¾ cups unbleached all-purpose flour and ½ teaspoon baking soda in medium bowl; set aside.
Heat 10 tablespoons unsalted 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 use heatproof spatula to transfer browned butter to large heatproof bowl. Stir remaining 4 tablespoons unsalted butter into hot butter until completely melted.
Add ½ cup granulated sugar, ¾ cup packed dark brown sugar, 1 teaspoon table salt, and 2 teaspoons vanilla extract to bowl with butter and whisk until fully incorporated.
Add 1 large egg and 1 large egg yolk and whisk until mixture is smooth with no sugar lumps remaining, about 30 seconds. Let mixture stand for 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 1¼ or and ¾ and or if using. Give dough final stir to ensure pockets remain.