In a saucepan over medium heat, melt two sticks of butter. Cook the butter for 5 to 8 minutes while whisking or stirring with a high temperature rubber spatula. The butter will crackle and foam at first as the liquid evaporates. Stir constantly, until it turns golden brown and the milk solids at the bottom are toasted. It should smell super buttery, rich and nutty, almost butterscotch-like. Perfect brown butter goes from caramel brown to burnt in a matter of seconds, so once you arrive at the pretty brown color, quickly and carefully pour the butter into a clean cool bowl to stop the cooking. Let the butter cool to below 100º before moving forward with the recipe.
Preheat your oven to 350ºF. In a bowl, combine the brown butter, white sugar, brown sugar and salt. Whisk together to work out any lumps, or until combined.
Mix in the eggs and vanilla. This can be done on low speed in an electric mixer, or by whisking by hand.
Sift together the flour and baking soda, then gently combine with a spatula until just incorporated. Do not overmix.
Fold in the chocolate chips.
Using a 2 ounce disher, scoop the dough onto baking sheets lined with parchment paper. This recipe should yield about 18 to 20 scoops. If you are using half sheet pans, place no more than 6 cookies on a sheet pan.
Bake for 12 to 15 minutes, until the edges and/or bottoms have lightly browned. Let them cool for about 10 minutes before serving.