Preheat oven to 350°F.
In the bowl of a stand-mixer, add melted butter and cocoa powder; blend until smooth.
Add flour and sugar and beat together. Add eggs and vanilla until just combined. (Batter will be thick)
Pour batter into a greased 13x9 inch baking dish and spread out evenly. Bake 25-35 minutes or until a toothpick inserted in center comes out clean. Let stand 15 minutes before frosting.
For the frosting: In a large bowl, beat all frosting ingredients together until smooth. Spread over warm brownies. Let cool completely before cutting and serving.