In a saucepan, melt butter. Remove from the heat. Stir in cocoa; 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 a greased 13x9-in. baking pan. Bake at 350° until a toothpick inserted in the center comes out clean, 25-28 minutes (do not overbake). Cool on a wire rack.
For frosting, in a large bowl, cream butter and confectioners' sugar until light and fluffy. Beat in cocoa and vanilla. Add enough milk until the frosting achieves spreading consistency. Spread over brownies. Cut into bars.