Prepare the Baking Pan: Grease an 8 × 8-inch baking pan to prevent the brownies from sticking.
Combine the Dry Ingredients: Sift the all-purpose flour, unsweetened cocoa powder, salt, and baking powder together in a mixing bowl. Set the mixture aside.
Cream the Butter and Sugar: In a separate large mixing bowl, beat the room-temperature butter and light brown sugar together until well combined and creamy.
Incorporate the Eggs and Vanilla: Add the eggs and vanilla extract to the butter-sugar mixture. Blend thoroughly until the ingredients are evenly incorporated.
Add the First Portion of Dry Ingredients: Add half of the prepared flour and cocoa mixture to the wet ingredients. Mix until combined.
Finish Mixing the Batter: Add the remaining dry ingredients to the bowl and mix until everything is just combined into a uniform brownie batter.
Fill the Baking Pan: Transfer the brownie batter into the prepared 8 × 8-inch baking pan. Spread it into the pan evenly.
Bake the Brownies: Place the pan in a preheated oven at 350°F (175°C) and bake for 20 minutes.
Cool and Slice: Allow the brownies to cool before cutting them into 16 equal squares.