Heat the white chocolate, milk, and 1 1⁄2 cups heavy cream in a heavy saucepan, stirring occasionally. When the mixture is hot and the chocolate is melted, distribute between 6 cups.
Meanwhile, whisk together 1 1⁄2 cups heavy cream and confectioners’ sugar. Beat until mixture forms stiff peaks. Garnish each cup with whipped cream and shaved chocolate.
