Stir together ⅓ cup cocoa powder and 2 Tablespoons hot coffee or water. Set aside for a minute or two to bloom.
Beat ¼ cup butter until smooth and fluffy. Add the cocoa mixture and mix until combined.
Stir in 2½ cups powdered sugar, ½ teaspoon vanilla extract, and 2 Tablespoons milk. Whip until smooth.
Spread over cooled brownies.
Notes
The recipe as written will cover a 9x13-inch pan of brownies. Double for sheet pan brownies or make a half recipe for an 8 or 9-inch square. Use the button above the ingredients in the digital recipe card to easily size your batch to what you need.