Place a rack near the center of the oven and preheat the oven to 350 degrees F. Line the bottom of a 9-inch cast iron skillet with parchment paper. Spray the sides and parchment paper with cooking spray. Set aside.
Place the butter in a microwave-safe bowl and zap in the microwave on 15 second intervals until the butter is half liquid and half semi-solid state. Let sit for 5 minutes at room temperature.
In a medium bowl, whisk together the flour, baking soda, and sea salt. Set aside.
In the bowl on an electric mixer fitted with the paddle attachement, cream the butter, brown sugar, and granulated sugar for 2 minutes. Add the vanilla extract. Add the eggs one at a time waiting until the previous one is completely mixed. Add the flour mixture to the bowl in 3 batches, waiting until the mixture is completely mixed before adding more, this takes about 2 minutes. Stop the mixer, scrape down the sides of the bowl and fold in the chocolate chips.
Dumb half the cookie dough onto the parchment lined cast iron skillet. Using your fingers or a rubber spatula, pat down the cookie dough into an even layer. Spread Nutella on top of the cookie dough, leaving a 1/2 - 1 inch border around the sides. Spread the rest of the cookie dough on top and gently pat down to even it out on all sides.
Place in the oven and bake for 20 minutes uncovered then cover with a piece of aluminum foil and continue to bake for and additional 10 minutes. (see notes). Remove from oven and allow to rest for at least one hour in order for the pieces to hold their shape when cut.