Chop the chocolate up finely if it's in a bar rather than morsels.
In a medium-sized saucepan, whisk together 2 teaspoons sugar, (Save ½ tsp. for the whipped cream), tapioca starch, and cocoa powder. Then pour in just a little milk and whisk until you have a smooth slurry with no lumps.
Stir in the remaining milk. Set the pan on medium heat. Stir constantly until it gets steamy (160℉/70℃ is good). Don't let it boil.
Stir in the chopped chocolate until it melts.
Keep the milk warm while you whip the cream with ½ teaspoon sugar.
Pour the hot chocolate into 2 warm mugs and top each with whipped cream.Add a little shaved chocolate for garnish, if you wish.
Video
Notes
To keep hot chocolate as warm as possible, serve it in a warm mug. I fill mine with boiling water and let it sit while I prepare the drink.