Add the chocolate chips, sugar and cocoa to a double boiler and heat, mixing, until melted and smooth. Add 2 cups of the milk to the melted chocolate mixture to temper the milk.
Fill a blender halfway with ice, add the chocolate mixture and remaining 2 cups milk and blend. Fill 4 glasses to the top with the mixture and top with whipped cream. Shave some chocolate over the top of each with a grater.