Preheat oven to 350°F. Line a 8”x8” inch pan with foil and spray the foil with nonstick cooking spray.
In the bowl of an electric mixer fitted with the paddle attachment beat the butter and sugar and well combined, about 1-2 minutes. Add the eggs and vanilla extract and mix until smooth.
Add the flour, cocoa, and salt and mix until just combined.
Spoon the batter into the prepared pan and smooth into an even layer.
Bake for 18-22 minutes or until a toothpick inserted in the center comes out with moist crumbs on it but no wet batter. Remove from the oven and let cool for 5 minutes.
While cooling make the frosting. Add the butter, powdered sugar, milk, and cocoa powder to a medium bowl. Using a hand mixer, beat until smooth and combined.
Frost the warm brownies and then let frosting set slightly before cutting and serving.
Notes
Cocoa powder: You can use dutch-process cocoa powder OR natural unsweetened cocoa powder for these brownies. The two cocoa powders are interchangeable as long as the recipe does not use baking powder or baking soda. Gluten-free brownies: To make these lunch lady brownies gluten-free use gluten-free flour rather than all purpose flour.Frosting tips: If you want a thinner frosting just add a splash of milk until you get your desired consistency. Storage: Store brownies in an airtight container for 5 days. They do not need to be refrigerated, but you're welcome to store them in the fridge.