In a small saucepan, whisk together granulated sugar, flour and cocoa until well combined.  Gradually stir in milk and whisk until smooth.  Cook over medium heat, stirring constantly until mixture thickens and boils.  Reduce heat to low and cook for two minutes, stirring continually.  Remove pan from heat and allow to cool completely.

In a large bowl, beat softened butter until creamy.  Gradually blend in the cooked mixture, vanilla and melted semi-sweet chocolate.

After the mixture is well combined, begin adding confectioner's sugar, one cup at a time, mixing well after each addition, until desired spreading consistency.