In a large saucepan, melt the butter over low heat. Once fully melted, increase the heat to low-medium to cook the butter, stirring frequently with a rubber spatula or wooden spoon. The butter will start popping and crackling and then start foaming. The part of the butter that will start browning is the milk solids which will be on the bottom of the pan. This is why you need to keep stirring and lifting the spatula or spoon out of the pan to see what stage it is at. Once you have nicely browned specks on the bottom of the pan, remove the pan from the heat and immediately pour the butter into a heatproof bowl to stop it from cooking any further. (Be careful not to overcook the butter. It can go from brown to burnt very quickly.) Allow the butter to cool to room temperature. Cover and refrigerate until hardened, at least an hour. (Brown butter can be made a day or two in advance and stored in the refrigerator.) Allow the brown butter to come to room temperature at least 30 minutes before mixing the dough.
In a small bowl, combine the flour, baking soda and salt.
In an electric mixer fitted with the paddle attachment, cream together the brown butter, sugar, brown sugar, milk, vanilla and vinegar. Add the eggs and beat until fully combined.
Add the dry ingredients and mix just until fully combined. Mix in the chocolate chips.
Preheat the oven to 375° F.
Spread the batter into a 9-inch by 13-inch pan. At this point, you can cover the pan and refrigerate it for up to 3 days before baking. Sprinkle sea salt on top and bake 24-26 minutes. The edges will be golden brown and start to pull from the sides of the pan.
Cool before slicing.