Melt the salted butter in a heavy saucepan over medium heat. Continue cooking over medium heat, stirring frequently until the butter is chestnut brown in color and has a nutty aroma. It is completely normal for the butter to sputter, bubble, and foam during the process. Pour into a heat-safe bowl or container and let cool for 10 minutes.

Preheat the oven to 350℉. Line a 9x9-inch pan with parchment paper, leaving the edges to hang over the sides.

Whisk together the slightly cooled brown butter and brown sugar. Add the egg and vanilla and whisk until smooth. Stir in the flour, baking powder, and salt, mixing just until no streaks of flour remain. Fold in the chocolate chips.

Transfer the batter to the prepared pan, spread into the corners, and level with a spatula. Bake in the preheated oven for 18-25 minutes or until golden around the edges. Sprinkle with flakey salt and then let cool for at least 10 minutes before lifting out of the pan using the parchment paper as handles. Slice into 16 bars once cooled. Enjoy!