Preheat oven to 350°F (175°C) and line a 9x13 inch pan with parchment. Melt butter in a light-colored saucepan over medium heat, stirring occasionally, until golden-brown specks appear, 5 to 7 minutes. Pour into a large bowl and cool for 10 minutes.

Whisk granulated sugar and brown sugar into the cooled brown butter until combined, about 1 minute. Add eggs and vanilla extract, whisk until glossy, about 30 seconds. Fold in flour, baking soda, and salt until no dry streaks remain, then fold in chocolate chips.

Scrape dough into the prepared pan and press into an even layer all the way to the corners.

Bake at 350°F (175°C) for 20 to 24 minutes, until the edges are deep golden brown and the center has just a little give when pressed.

Cool in pan for 15 minutes, lift out onto a cutting board, slice into slabs, and serve warm with a pinch of flaky sea salt scattered over the top.