Preheat the oven to 350 degrees F (180 degrees C). Line an 8x8-inch baking dish with parchment paper, grease the parchment, and coat with half the coconut flakes, scattering evenly over the bottom and sides of the baking dish; set aside.
Melt butter in a small saucepan or in the microwave. Whisk melted butter and brown sugar together in a large bowl. Add eggs, vanilla extract, and coconut extract, and whisk until well combined.
Fold in flour and baking powder with a spatula, just until combined and no dry flour is showing. Pour batter into the prepared baking dish and sprinkle remaining coconut evenly on top. Cover loosely with foil.
Bake covered in the preheated oven for 25 minutes. Remove foil and bake until coconut is lightly toasted, 10 to 15 minutes more.
Let dessert bars cool for at least 15 minutes before cutting; the longer they cool, the more they will set, and the easier they will be to cut.
