Preheat your oven to 350°F (175°C). Line a 9×13-inch baking pan with parchment paper or lightly grease it.

In a large saucepan over medium heat, melt 1 cup of unsalted butter. Stir in 2 cups of granulated sugar until it is fully mixed. Remove from heat.

Let the butter-sugar mixture cool a little. Then, add 4 large eggs, one at a time, mixing well after each addition. Stir in 1 teaspoon of vanilla extract.

In a separate bowl, mix together 1 cup of flour, 1 cup of cocoa powder, 1 teaspoon of baking powder, and 1/2 teaspoon of salt. Gradually add these dry ingredients to the wet mixture, stirring until just combined.

Pour the brownie batter into the prepared pan and spread it evenly.

Bake for 25-30 minutes. A toothpick inserted should come out with a few moist crumbs but no wet batter.

While the brownies cool, prepare the frosting. Beat 1/2 cup of softened butter and 2/3 cup of cocoa powder until smooth.

Gradually add 3 cups of powdered sugar and 1/3 cup of milk, mixing until creamy.

Stir in 1 teaspoon of vanilla extract.

Once the brownies are fully cooled, spread the frosting evenly over the top.

Let the frosting set before cutting the brownies into squares.