Pour the light cream or half and half into a medium sauce pot. Add the milk, chocolates, and corn syrup and stir with a wooden spoon.
Make Ahead Tip:
Let the hot chocolate cool and pour the mixture into an ice cube tray. Freeze the hot chocolate overnight. When you are in the mood for heaven, pop some hot chocolate cubes into a mug and microwave for about 5-10 minutes checking on it every few minutes.