Preheat oven to 350°F with a rack just below the middle of the oven (in the lower third). Grease a 10-inch (large recipe) or 8-inch (small recipe) cast iron skillet and set it aside.
In a large bowl using a hand mixer or stand mixer with the paddle attachment, beat butter and both sugars for 1 minute, until light and creamy. Add egg, egg yolk, and vanilla extract and beat to combine, scraping the sides of the bowl as needed.
In a separate bowl, combine flour, baking soda, and salt. Add dry ingredients to the butter mixture and beat until thoroughly combined. Using a rubber spatula, stir in most of the chocolate chips, reserving a couple tablespoons for topping the cookie.
Scoop the dough into the cast iron skillet and press it into an even layer (I moisten my fingertips with water to easily press it in; it will be sticky). Sprinkle the reserved chocolate chips over the top. Bake the large skillet for 25-30 minutes and the small skillet for 18-23 minutes. The center should still be a bit underdone, the edges should be set, and the whole cookie should be golden brown. Be careful not to overbake. Place on a wire rack and allow to cool for at least 30 minutes, preferably an hour. Serve warm with ice cream.
