Place chocolate in heavy saucepan on very low heat. Stir constantly until just melted; set aside to cool.
Combine in large bowl, with mixer at low speed, sugar, butter, milk and vanilla. Beat at medium speed for 1 to 2 minutes, until creamy. Add cooled chocolate and beat until combined. If desired, add more milk until frosting is spreading consistency.
Makes enough to fill and frost a 2-layer cake, 13x9x2-inch sheet cake or 24 cupcakes.
To melt chocolate in the microwave, place it in a microwaveable bowl on HIGH for 1 to 2 minutes or until almost melted, stirring halfway through heating time. Remove from microwave; stir until completely melted.