1. Place a rack in lowest position in oven; preheat to 190°C. Coarsely chop chocolate but leave some whole.
2. Mix brown sugar, granulated sugar, butter, and salt in a large bowl until no large lumps remain, about 1 minute. Stir in egg and vanilla until egg is incorporated and mixture is very loose and resembles cake batter, about 30 seconds. Add flour and baking soda and mix until dough comes together and no streaks remain, about 30 seconds. Stir in ¾ cup chocolate, reserving remaining chocolate, until evenly distributed.
3. Scrape batter into a 26cm cast-iron skillet (or use a stainless steel skillet coated with nonstick vegetable oil spray). Pat batter into skillet with damp hands, pressing into an even layer so dough extends to sides of pan. Scatter remaining chocolate over cookie and sprinkle with sea salt.
4. Bake cookie until outer edges are browned and slightly puffed, 20–25 minutes (15–18 minutes for stainless steel). Let cool in skillet 1 hour (if you can resist!). Serve in skillet or turn out; cut into wedges. Don't forget the ice cream!