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, 1-3 minutes. Be careful not to let it burn!

Remove the skillet from the heat and transfer the browned butter to a large heatproof bowl.

Stir the remaining 4 tablespoons of 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.

Line 2 large baking sheets with parchment paper, or coat them with cooking spray.

In a shallow baking dish or pie plate, mix the granulated sugar and 1/4 cup packed brown sugar; set aside.

Whisk the flour, baking soda, and baking powder together in a medium bowl; set aside.

Add the remaining 1 3/4 cups brown sugar along with the salt to 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, egg yolk, and vanilla and mix until fully incorporated, about 30 seconds.

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.

Form the dough into 1 1/2 inch balls, and roll them in the sugar mixture to coat. Place them on the prepared baking sheets, about 2 inches apart.

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, 8-10 minutes. Do not over bake!

Cool for 1-2 minutes on the baking sheets and then remove to a wire rack to cool completely.