In a small bowl or measuring cup with a spout, whisk together ½ cup milk and cornstarch until well incorporated.
In medium saucepan over medium-high heat, whisk remaining 1 cup of the milk with cream and sugar. Heat through, whisking occasionally, until mixture starts to bubble around the edges.
Add the cornstarch mixture to saucepan and whisk constantly until heated through, about 1 minute.
Reduce heat to medium-low, add chopped chocolate, and whisk until completely melted, and mixture thickens to coat a spoon, about 5 minutes.
Slowly add pomegranate juice while continuing to whisk until fully incorporated and mixture is heated through.
Pour into mugs or glasses, top generously with whipped cream and sprinkles of shaved chocolate.