2cups(284g)unbleached all-purpose flour plus 2 tablespoons (15 g)
Heat 10 tablespoons butter in a 10-inch stainless steel (not nonstick) skillet or small uncoated saucepan over medium heat until melted, about 2 minutes. Continue to cook, swirling pan constantly until butter is dark golden brown and has nutty aroma, 1 to 3 minutes. Browned butter can burn easily and quickly so keep a close eye on it!
Remove the skillet or pot from the heat and transfer the browned butter to a large heatproof bowl. Stir the remaining 4 tablespoons butter into the hot butter to melt; set aside for 15 minutes.
Meanwhile, adjust an oven rack to the middle position and heat the oven to 350 degrees F. Line 2 large (18 by 12-inch) baking sheets with parchment paper, silpat liners or lightly coat them with cooking spray.
In a shallow baking dish or pie plate, mix the granulated sugar and 1/4 cup packed brown sugar, rubbing between your fingers, until well combined; set aside. Whisk flour, baking soda, and baking powder together in a medium bowl; set aside.
Add remaining 1 3/4 cups brown sugar and salt to the bowl with the cooled butter and mix until no sugar lumps remain, about 30 seconds. Scrape down the sides of the bowl with a rubber spatula; add the egg, yolk, and vanilla and mix until fully incorporated, about 30 seconds. Scrape down the bowl.
Add the flour mixture and mix until just combined, about 1 minute. Give the dough a final stir with a rubber spatula to ensure that no flour pockets remain and the ingredients are evenly distributed.
Divide the dough into 24 portions, each about 2 tablespoons, forming balls about 1 1/2 inches in diameter. Working in batches, toss the balls in the reserved sugar mixture to coat and set them on the prepared baking sheet, spacing them about 2 inches apart, 12 dough balls per sheet. (Smaller baking sheets can be used, but it will take 3 batches.)
Bake one sheet at a time until cookies are browned and still puffy and edges have begun to set but the centers are still soft (cookies will look raw between cracks and seem underdone - don't overbake), 11-13 minutes. Cool the cookies for 1-2 minutes on the baking sheets and then remove to a wire rack to cool completely.
Butter: if you plan to use unsalted butter, increase the salt in the recipe to 1/2 teaspoon. Brown Sugar: I wouldn't recommend substituting light brown sugar - because the brown sugar makes up the majority of flavor in the cookies, the dark brown sugar adds depth and substance.