Melt the butter in a light-colored saucepan over medium heat. Continue cooking, stirring occasionally, until the butter browns and a nutty aroma appears. This usually takes 5-7 minutes. Once browned, immediately remove from heat and pour into a heat-safe bowl to cool slightly. Scrape all brown bits from the bottom of the pan.

In a large bowl, combine the cooled brown butter with dark brown sugar and granulated sugar. Whisk until smooth and well combined.

Add the egg and vanilla extract to the sugar mixture. Whisk vigorously for about 1 minute until the mixture is lightened in color and fluffy.

In a separate bowl, whisk together the all purpose flour, baking powder, and kosher salt.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Be careful not to overmix.

Fold in the semisweet chocolate chips until evenly distributed. Press the dough into an 8x8 inch baking pan lined with parchment paper, leaving an overhang on two sides.

Bake at 350°F (175°C) for 20-25 minutes, or until the edges are golden brown and the center is set but still slightly soft. A toothpick inserted into the center should come out with moist crumbs, not wet batter. Sprinkle with extra chocolate chips and flaky sea salt immediately after removing from the oven. Let cool completely in the pan before slicing into bars.