Preheat your oven to 350°F (175°C). Line a 9-inch square baking pan with foil, leaving a bit of foil hanging over the sides for easy removal.
In a medium bowl, cream together the melted butter and sugar until smooth. Add the eggs and vanilla extract, mixing until fully combined.
Gradually add the cocoa powder and flour to the wet mixture, folding gently until the batter is smooth and even.
Pour the batter into the prepared baking pan, spreading it into an even layer.
Bake in the preheated oven for about 20 minutes, or until a toothpick inserted into the center comes out with just a few moist crumbs. Be careful not to overbake—the center should remain fudgy.
While the brownies are cooling, prepare the frosting. In a small bowl, mix together the cocoa powder, powdered sugar, softened butter, and milk. Adjust the consistency as needed: add more milk if the frosting is too thick, or more powdered sugar if it’s too thin.
Spread the frosting evenly over the warm brownies so some of it melts slightly into the top, creating a rich, fudgy layer.
Once cooled, use the overhanging foil to lift the brownies out of the pan. Cut into squares and serve.
Enjoy these classic, fudgy, chocolatey brownies just like the ones from the cafeteria—perfect for dessert, snacks, or a sweet treat anytime!
Enjoy!