A Giant Chocolate Chip Skillet Cookie

Adjust an oven rack to the upper-middle position and preheat the oven to 375 degrees. Melt 9 tablespoons butter in a 12-inch cast-iron skillet over medium heat. Continue to cook, stirring constantly, until butter is dark golden brown, has a nutty aroma, and the bubbling has subsided some, about 5 minutes. Transfer to a large bowl and stir remaining 3 tablespoons into hot butter until completely melted.
Whisk 3/4 cup dark brown sugar, 1/2 cup granulated sugar, 2 teaspoons pure vanilla extract, and 1 teaspoon kosher salt into melted butter until smooth. Whisk in 1 large egg and 1 large egg yolk until smooth, about 3 seconds. Let the 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.
Whisk 1 3/4 cups all-purpose flour and 1/2 teaspoon baking soda in a separate bowl, then stir flour mixture into butter mixture until just combined, about 1 minute. Stir in 1 cup chocolate chips (and if using, 3/4 cup hazelnuts), making sure no flour pockets remain.
Wipe skillet clean with paper towels. Transfer dough to the now-empty and wiped down skillet and press into an even layer across the pan with a spatula. Transfer skillet to the preheated oven and bake until cookie is golden brown and edges are set, about 20 minutes. Using potholders, transfer the skillet to a wire rack and let cookie cool for 30 minutes. Slice cookie into wedges and serve.

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