Preheat your oven to 350°F (175°C).
In a medium saucepan, melt the butter over low heat. Let it cool until warm.
In a large mixing bowl, combine the melted butter with the light brown sugar and granulated sugar. Whisk until smooth and creamy.
Add the egg, egg yolk, and vanilla extract to the sugar mixture. Whisk until fully incorporated.
In a separate bowl, whisk together the flour, baking soda, and salt. Gradually add this dry mixture to the wet ingredients, stirring until just combined.
Using a rubber spatula, fold in the chocolate chips until evenly distributed.
Pour the cookie dough into your cast iron skillet, spreading it out evenly.
Bake in the preheated oven for 25-30 minutes or until the edges are golden brown and the center is just set.
Let the skillet cookie cool for about 10 minutes before slicing. Serve warm, ideally with a scoop of vanilla ice cream!