Preheat oven to 350 F and grease an 8x8-inch pan with nonstick baking spray.
Melt butter in medium saucepan over medium heat. Continue cooking until butter stops foaming and there are brown bits on the bottom of the pan, about 5 minutes.
Transfer butter to a large mixing bowl, then add in brown sugar and whisk until well combined. Set aside to cool for 5 minutes.
Add eggs, whisking after each addition for about 10 strokes, then add vanilla and stir to combine.
In a separate bowl, whisk together flour, baking powder, and salt. Pour into the batter mix, then whisk only until a few pockets of flour remain. Fold in chopped chocolate, then turn batter into prepared pan.
Bake for 26-28 minutes, or until top is light golden brown. Cool in pan on wire rack, then transfer from pan and cut into 2x2 squares.