12 tablespoons unsalted butter, cut into tablespoon sized slices
1 3/4 cups dark brown sugar
1/2 teaspoon salt
1 egg yolk
1 tablespoon vanilla extract
2 1/2 cups all-purpose flour
1/2 teaspoon baking soda
1/4 teaspoon baking powder
Sugar Dredging Mixture
1/4 cup dark brown sugar
2 tablespoons sugar
Fleur de sel, Maldon, sea salt, or Kosher salt for sprinkling (don't use regular table salt, it won't taste right.)
1 Preheat oven to 375°F and line baking sheets with parchment paper. Sift together the flour, baking soda, and baking powder and set aside. Mix together the sugar dredging mixture in another bowl and set aside.
2 Place 10 tablespoons of butter into a thick-bottomed skillet over medium heat. The butter will foam a bit before subsiding. Once the butter takes on a tan color and begins to smell nutty take it off of the heat. Add the other two tablespoons of butter and mix it in until it melts.
3 Pour the brown butter into a mixing bowl fitted with a paddle attachment. Add the brown sugar and salt and mix. Add the egg, egg yolk, and vanilla extract and mix together, scraping down the sides and bottom of the bowl at least once. Add the flour mixture in three increments being sure to scrape down the sides and bottom once or twice. Mix just until the flour is incorporated. The dough will be very thick.
4 Take 1/2 to full tablespoon-sized pieces of dough (you can make them a bit bigger or smaller to your liking, just make sure the pieces of dough are all the same size) and gently roll them into ball shapes. Dredge them in the sugar dredging mixture until well-coated. Place on the baking sheet and sprinkle with a little bit of the sprinkling salt (be reserved with the salt as very little goes a long way).
5 Bake for 10-12 minutes or until the edges have browned a bit. Be careful not to over-bake. Allow to cool on the sheet for one minute before transferring to a wire rack to cool completely. Tastes best with a glass of milk for dipping.