Preheat the oven to 355°F (180°C) and line two baking sheets with parchment paper.
Place the white and brown sugar in a mixing bowl. Set aside.
Melt the butter in a light-colored pan over medium-low heat. Stir occasionally until the butter turns golden brown and has a nutty aroma.
Once browned, immediately pour the butter into the bowl with the sugar. Whisk well to combine.
Add the vanilla extract and the egg, and whisk until emulsified.
Sift in the flour, salt, and baking soda, and mix just until no dry ingredients are visible.
Fold in the chocolate chips.
Scoop 14 even dough balls onto the prepared baking sheets. Bake one batch at a time for 10-12 minutes, or until the cookies have spread and the edges are set.
Remove from the oven and, if desired, top with flaky sea salt. Let the cookies rest on the sheet for a couple of minutes, then transfer them to a cooling rack to cool completely. Bake the second batch.