Preheat your oven to 350°F. Put a 6-inch cast-iron skillet in the oven for at least 10 minutes.
In a bowl, whisk together melted butter, dark brown sugar, and granulated sugar until combined, about 1 minute. Add an egg, an egg yolk, and vanilla, then mix until combined. Stir in baking soda and salt. Fold in flour until just mixed. Add chocolate chips and salted caramel sauce, folding gently to create ribbons.
Carefully take out the hot skillet, butter it lightly, and spoon in the dough. Spread it to the edges. Bake for 18-22 minutes until the edges are golden brown, but the center is still shiny and jiggly.
Let it rest for 3-4 minutes. Drizzle warm, salted caramel over the top, sprinkle with sea salt, and add two scoops of vanilla ice cream. Serve immediately with spoons!