Prepare the Batter. Start by preheating your oven to 350°F and greasing a 9x13 inch baking pan. Melt the butter and mix it with the sugar, cocoa powder, eggs, and vanilla extract until smooth. Gently fold in the flour and salt until just combined. Do not overmix.
Bake the Brownies. Pour the batter into the prepared baking pan and spread it evenly. Bake for 20-25 minutes or until the edges are set and a toothpick inserted into the center comes out with a few moist crumbs. Cool completely in the pan.
Make the Glaze. In a mixing bowl, whisk together the powdered sugar, cocoa powder, milk, and melted butter until smooth. Pour the glaze over the cooled brownies and spread it evenly.
Slice and Serve. Let the glaze set for a few minutes before cutting the brownies into squares. Enjoy your classic lunchroom treat!