Preheat oven to 350F (180C). Grease with butter a 8×8 inch (20x20cm) pan and line with parchment paper.
Place butter into a small saucepan and cook over medium heat, stirring occasionally until butter gets a nutty brown color It may take few minutes.
Sieve the butter into a large bowl and let cool to room temperature.
In a medium bowl whisk together flour with baking powder and salt and set aside until ready to use.
Add brown sugar over the melted brown butter and mix to combine. Incorporate egg and then add vanilla extract.
Add flour mixture and mix to combine. Fold the chocolate chips and transfer the batter into the prepared pan.
Bake for 20-25 minutes, until a toothpick inserted into the center of the cake comes out clean.
Let it cool for at least 15 minutes before cutting it into squares. Enjoy!.