This dessert was inspired by the Frozen Hot Chocolate at Serendipity, a restaurant in New York City.
Whip 1/2 cup cream, and set aside.
Place the milk, remaining 3/4 cup cream, sugar, cocoa, and malted-milk powder in the jar of a blender, and blend until smooth and frothy.
With the motor running, add ice cubes, a few at a time, until the mixture is thick and smooth. Pour the mixture into tall glasses, and top with whipped cream and chocolate shavings, if desired.