Microwave chocolate pieces and 1/4 cup whipping cream in a 1-quart microwave-safe bowl at MEDIUM (50% power) 1 minute and 10 seconds. Whisk until chocolate melts and mixture is smooth. (Do not overheat mixture.)
Beat butter and 1 cup powdered sugar at low speed with an electric mixer until blended. Add remaining 5 cups powdered sugar alternately with remaining 1/4 cup whipping cream, beating at low speed until blended after each addition. Add white chocolate mixture and vanilla; beat at medium speed until spreading consistency.