Brown Butter Chocolate Chip Skillet Cookie

• Adjust oven rack to upper-middle position and preheat oven to 375° F.
• In a 12" cast-iron skillet over medium heat, melt 9 tablespoons of the butter. Continue to cook, stirring fairly constantly, until butter is dark golden brown and has a nutty aroma. I like to use a large stainless steel spoon, so I can see how the butter is browning, as it’s harder to see the browning against the dark skillet. After about 5 minutes, a bunch of smallish bubbles will form and then subside – this is when you will know the butter is done browning. With a rubber spatula, transfer brown butter to a large bowl. Stir in remaining 3 tablespoons of the butter into the hot butter until completely melted.
• Add brown sugar, sugar, vanilla, and salt to melted butter and whisk until smooth. Then whisk in egg and yolk until smooth, about 30 seconds. Let mixture sit for 3 minutes, then whisk for 30 seconds. Repeat process of resting and whisking 2 more times until mixture is thick, smooth, and shiny. This process allows the sugar to dissolve more, giving better flavor and texture.
• In a medium bowl, whisk flour and baking soda together. Then stir flour mixture into butter mixture until just combined, about 1 minute. Fold in chocolate chips and chocolate chunks.
• Wipe skillet with paper towels to remove any excessive butter left behind. Transfer cookie dough to skillet and press into an even layer with a rubber spatula. Sprinkle a few more chocolate chips and chocolate chunks over the top, pressing them in just slightly, for a pretty effect.
• Transfer skillet to oven and bake until cookie is golden brown and edges are set, about 18 minutes or so, rotating skillet halfway through baking. Do not over bake – the cookie will firm up as it cools. Using potholders, transfer skillet to wire rack. If desired, sprinkle immediately with sea salt flakes. Let cookie cool for at least 30 minutes if serving warm, without chocolate buttercream. Let cookie cool completely if decorating with chocolate buttercream.

for the chocolate buttercream (optional):

• In the bowl of a stand mixer fitted with a paddle attachment, beat the butter on medium-high speed until creamy and lightened in texture, about 2 minutes. Add powdered sugar, cocoa powder, espresso powder, heavy cream, kosher salt, and vanilla extract. With mixer on low speed, beat until just combined. Increase speed to high and beat for 30 seconds. Scrape down mixer bowl and then beat on high for another 30 seconds. If buttercream is thinner than you’d like, add a bit more powdered sugar, 1/4 cup at a time. If thicker than desired, add more cream, a tablespoon at a time.
• When chocolate chip cookie skillet has completely cooled, fit a pastry bag with a large star tip (this is the one I used) and fill with chocolate buttercream. Pipe buttercream around perimeter of cookie skillet. If you want to add sprinkles, add them as soon as you finish piping the buttercream, so the sprinkles will "stick".