1. Combine chocolate and butter in a small heavy saucepan. Place the pan over low heat just until melted, stirring occasionally. Remove from heat.
2. Combine powdered sugar, milk and vanilla in a medium-size bowl; stir together until smooth. Stir in the chocolate mixture until well blended. Set the bowl in a pan of ice water and beat with a wooden spoon until the frosting is thick enough to spread and hold its shape.