The most efficient way to bake these cookies is to portion and bake half of the dough. While the first batch is in the oven, the remaining dough can be prepared for baking. Avoid using a nonstick skillet to brown the butter. The dark color of the nonstick coating makes it difficult to gauge when the butter is sufficiently browned. Use fresh brown sugar, as older (read: harder and drier) brown sugar will make the cookies too dry.
Makes 2 Dozen Cookies
1. Heat 10 tablespoons butter in 10-inch skillet over medium-high 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. Remove skillet from heat and transfer browned butter to large heatproof bowl. Stir remaining 4 tablespoons butter into hot butter to melt; set aside for 15 minutes.
2. Meanwhile, adjust oven rack to middle position and heat oven to 350 degrees. Line 2 large (18 by 12-inch) baking sheets with parchment paper. In shallow baking dish or pie plate, mix granulated sugar and 1/4 cup packed brown sugar, rubbing between fingers, until well combined; set aside. Whisk flour, baking soda, and baking powder together in medium bowl; set aside.
3. Add remaining 1 3/4 cups brown sugar and salt to bowl with cooled butter; mix until no sugar lumps 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.
4. Divide dough into 24 portions, each about 2 tablespoons, rolling between hands into balls about 1 1/2 inches in diameter. Working in batches, toss balls in reserved sugar mixture to coat and set on 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.)
5. 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; see photo below), 12 to 14 minutes, rotating baking sheet halfway through baking. Do not overbake.
6. Cool cookies on baking sheet 5 minutes; using wide metal spatula, transfer cookies to wire rack and cool to room temperature.
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