Chop the chocolate into small pieces and melt in a small heavy saucepan or in the top of a double boiler over simmering water. Stir occasionally until melted. Add the hot chocolate mix and sugar, stirring constantly until blended.
Remove from heat and slowly add 1/2 cup of the milk, stirring until smooth. Cool to room temperature.
In a blender, place the remaining 1 cup of milk, the chocolate mixture, and the ice. Blend on high speed until smooth and the consistency of a frozen daiquiri. Pour into a giant goblet and top with whipped cram and chocolate shavings.