12 T unsalted butter
1/4 cup granulated sugar
2 cups packed dark brown sugar
2 cups plus 2 T flour (I use whole wheat pastry flour)
1/2 tsp baking soda
1/4 tsp baking powder
1/2 tsp salt
1 large egg
1 large egg yolk
1 T vanilla
Heat 10 T butter in a 10-in skillet over medium-high heat until melted, about 2 minutes. Continue to cook, swirling pan constantly until butter is dark golden brown and has a nutty aroma, 1 to 3 minutes. Remove skillet from heat and transfer browned butter to a large heatproof bowl. Stir remaining 4 T butter into hot butter to melt; set aside for 15 minutes.
Adjust oven rack to middle position and heat oven to 350 degrees. Line 2 large baking sheets with parchment paper. In shallow baking dish or pie plate, mix granulated sugar and 1/4 cup brown sugar, rubbing between fingers, until well combined; set aside. Whisk flour, baking soda, and baking powder together in medium bowl; set aside.
Add remaining 1 3/4 cups brown sugar and salt to bowl with cooled butter; mix until no sugar clumps remain, about 30 seconds. Scrape down sides of bowl with rubber spatula; add egg, yolk, and vanilla and mix until fully incorporated, about 30 seconds. Scrape down bowl. Add flour mixture and mix until just combined, about 1 minute. Give dough final stir with rubber spatula to ensure that no flour pockets remain and ingredients are evenly distributed.
Divide dough into 24 portions, each about 2 T, rolling into balls about 1 1/2 inches in diameter (I used a small cookie scoop and made about 20 portions). Roll the balls in the reserved sugar mixture to coat and set on baking sheet, about 2 inches apart.
Bake one sheet at a time until cookies are browned and still puffy and edges have begun to set but centers are still soft (cookies will look raw between cracks and seem underdone), 12 to 14 minutes, rotating baking sheet halfway through baking. Do not overbake.
Cool cookies on baking sheet 5 minutes; transfer to cooling rack to cool to room temperature.