Preheat oven to 350 F. Grease a 9x13-inch baking pan. Set aside.
In a saucepan, melt butter.
Remove from the heat. Stir in cocoa. Set aside to cool.
In a large bowl, beat eggs and sugar until blended.
Combine flour, baking powder and salt; gradually add to egg mixture.
Stir in vanilla and the cooled chocolate mixture until well blended.
Spread into prepared baking pan. Bake for 20-28 minutes, or until a toothpick inserted in the center comes out with a few fudgy crumbs (do not overbake).
Cool on a wire rack.
For frosting, in a large bowl, cream butter and powdered sugar until well-combined.
Beat in cocoa and vanilla.
Add enough milk until the frosting achieves spreading consistency.
Spread frosting over cooled brownies.
Store, covered, in the fridge.
Notes
For the best results, chill brownies before serving.