To brown the butter, place it in a small saucepan and cook it over medium heat. Swirl occasionally for 8-10 minutes until the butter becomes foamy and fragrant with little brown flecks throughout. Once it turns brown and smells nutty, remove it from the heat and pour it into a large heat-proof bowl. Let the butter cool down for a couple of minutes.
Preheat your oven to 175°C (350°F).
Place the skillet with the brown butter back over low heat and stir in the brown sugar and granulated sugar. Mix until well combined and let it cool for a few minutes.
Mix the eggs and vanilla extract well into the brown butter and sugar mixture.
Sprinkle the all-purpose flour, baking soda, and salt over the wet ingredients in the skillet. Stir until just combined, being careful not to overmix.
Gently fold the chocolate chips into the cookie dough until evenly distributed throughout the skillet. Press the cookie dough evenly around the skillet.
Place the skillet in the preheated oven and bake for 25-30 minutes or until the edges are golden brown and crisp and the centre is slightly gooey.
Allow the cookie skillet to cool for a few minutes before slicing. This will help the cookie set slightly while maintaining its gooey centre. Optional: Sprinkle with sea salt.
Serve with a scoop of your favourite ice-cream.
Notes
Don't have time to make brown butter? No problem; if you don't want to brown the butter, you can simply melt it in the pan and add the sugar. Brown butter adds a nutty, rich flavour to the cookie skillet, but it's not necessary.