Prepare the Baking Pan: Preheat the oven to 350°F (175°C). Grease an 8 × 8-inch square baking pan with butter or line it with parchment paper to prepare it for the batter.
Combine the Butter and Sugar: In a large mixing bowl, whisk together the melted butter and white sugar until thoroughly combined.
Incorporate the Eggs and Vanilla: Add the room-temperature eggs and vanilla extract to the butter-sugar mixture. Beat well until the ingredients are fully incorporated. Thoroughly mixing the eggs helps create the brownies' characteristic crackly crust. Mix the Dry Ingredients: Add the cocoa powder, all-purpose flour, baking powder, and kosher salt to the bowl. Stir until the dry ingredients are just incorporated, taking care not to overmix the batter.
Fold in the Coconut and Chocolate Chips: Add the sweetened flaked coconut and ½ cup semi-sweet chocolate chips. Stir until they are evenly distributed throughout the brownie batter.
Fill the Baking Pan: Transfer the batter to the prepared pan and spread it evenly. If desired, sprinkle the top with the additional 1–2 tablespoons of coconut and 1–2 tablespoons of chocolate chips.
Bake the Brownies: Place the pan in the preheated oven and bake for 24 minutes, or until the center is set. Avoid relying on the baking time alone; check that the middle has set before removing the pan from the oven.
Cool and Slice: Allow the brownies to cool at least slightly before cutting them into 16 squares. This brief cooling period makes them easier to slice and serve.