Grease a 6-inch or 8-inch cast iron skillet with butter. Set aside.

In a medium skillet, melt butter over medium-low heat, stirring nearly continuously. Butter will melt, then begin to foam. It will then begin to turn golden brown and smell nutty. As soon at the butter begins to turn brown, take the pan off the heat, and continue to stir for about 1 minute, to ensure carryover heat doesn't continue to cook and subsequently burn the already browned butter. Transfer to a small bowl, cover with plastic wrap, and let cool to room temperature, about 1-2 hours.

When the butter has cooled down and started to solidify slightly, add the butter to a large mixing bowl. Add the sugars, and cream the butter and the sugars until light and fluffy, about 3 minutes on medium high. Scrape down the side of the bowl.

Add the egg and vanilla and mix until completely incorporated. Scrape down the bowl with a spatula. Combine the flour, soda and salt in another bowl with a whisk to combine. With the machine on low, slowly add the flour. Mix until just combined, taking care not to over mix. With a spatula, fold in the caramel bits and dark chocolate chunks.

Press about 1/3 of the dough into the bottom of prepared skillet (the entire bottom and sides of the skillet should be covered with dough). Fill with caramel sauce. Top with more dough until the top is completely covered and the caramel is sealed inside, you may have some left over - I had about 1 cup of dough remaining (see notes). Sprinkle the top of the cookie with flaky salt. Cover with foil and refrigerate for at least 30 minutes, or up to 3 days.

When you’re ready to bake, preheat oven to 350ºF.

Bake for 18-20 minutes or until golden brown on top. Serve immediately with ice cream and more caramel sauce if desired.