Preheat oven to 350° F.
Brown the butter. (This can burn suddenly, so make sure you keep your eye on it!) Melt butter in a saucepan over medium-low heat, stirring and scraping the bottom of the pan occasionally, until totally melted. As it heats up, the butter will pop and fizz. You will see little specks of brown start to form; these are milk solids and they are part of what give brown butter its amazing, nutty flavor. Once the butter is an amber color and stops popping, take it off the heat immediately. Transfer to a bowl of a stand mixer and let it chill in the freezer just until it cools down a bit.
In a medium bowl, whisk together flour, salt, and baking soda.
In the bowl of a stand mixer, cream together the sugars and the cooled butter on medium-low speed until combined. Mix in vanilla and egg until it becomes lighter in color and fluffier.
Add the dry ingredients and chocolate chips into the bowl and mix in just until the last streaks of flour disappear.
Line two sheet pans with parchment paper. Using a 2-tablespoon scoop, portion out the dough onto the sheets, leaving around 2 inches between each ball. They spread a bit.
Chill the portioned dough in the fridge for 10-15 minutes.
Bake on the middle racks for 6 minutes, then switch and rotate the pans positions, giving each a firm *thwap* on the counter. (This is the famous Sarah Kieffer technique for pan-banging cookies.) Bake for 6 more minutes.
Transfer cookies to a wire rack to cool.