In a blender, combine the milk, heavy cream, chocolate syrup, cocoa powder, powdered sugar, and vanilla extract. Blend until smooth and well combined.
Add the ice to the blender and blend until the mixture is thick and slushy. You may need to stop and scrape down the sides of the blender to ensure everything is mixed well.
Taste the mixture and adjust sweetness if desired by adding more powdered sugar or chocolate syrup.
Pour the frozen hot chocolate into serving glasses.
Top each glass with a generous dollop of whipped cream and sprinkle with chocolate shavings or mini marshmallows for garnish.
Serve immediately with a straw or spoon.