Heat oven to 350°F. Grease an 8x8 pan or line with parchment paper.
Combine ½ cup butter and 2 ounces chocolate in 2-quart saucepan. Cook over medium heat, stirring constantly, until melted (3 to 5 minutes). Stir in all remaining brownie ingredients until well mixed.
Spread batter evenly into greased 8 inch square baking pan. Bake for 23 to 27 minutes or until brownies begin to pull away from sides of pan.
Frosting
Combine ¼ cup butter, milk and 1 ounce chocolate in same saucepan. Cook over medium heat stirring occasionally until mixture comes to a full boil. 1 to 2 minutes. Remove from heat. Add powdered sugar, beat until smooth. Stir in vanilla. Spread over warm brownies. Cool completely. Cut into squares.Please see notes before beginning.
Notes
When cooking brownie mixture. Be certain to stir, but do not whip. As this can separate the butter and yield a greasy brownie.For the frosting: Do not boil past 2 minutes as this can cause the butter to separate and make it greasy.