Begin by preheating your oven to 350 degrees F (175 degrees C). Thoroughly grease a 9x13-inch baking pan to ensure easy removal of the brownies once baked.

In a spacious mixing bowl, combine the white sugar, all-purpose flour, melted butter, eggs, cocoa powder, vanilla extract, baking powder, and salt. Stir these ingredients together until the mixture is smooth and uniformly combined. This will form the rich, chocolatey batter essential for luscious brownies.

Pour the batter into the greased pan, using a spatula to spread it evenly. Garnish the surface with walnut halves, pressing them gently into the batter to anchor them.

Place the pan in the preheated oven and bake for 20 to 30 minutes. The brownies are done when the top appears dry and the edges start to pull away from the sides of the pan. Allow the brownies to cool in the pan before cutting them into squares, ensuring they hold their shape when served.