Melt first 4 ingredients in a 2-quart saucepan over medium-low heat, stirring 5 minutes or until mixture is smooth.
Transfer chocolate mixture to a large bowl. Place the bowl into a larger bowl filled with ice and water. Gradually add powdered sugar, beating at low speed with an electric mixer. Increase speed to medium-high, and beat 5 minutes or until frosting is cool, thick, and spreadable. Stir in 1 tablespoon vanilla.