In a saucepan off heat, whisk cocoa powder, starch, sugar, and a pinch of salt. Gradually whisk in cold milk to form a smooth mixture with no lumps.

Set over medium heat and cook, whisking constantly, until the mixture thickens and turns glossy.

Remove from heat and whisk in the finely chopped chocolate until completely melted and silky.

Adjust thickness with a splash of milk if needed. Serve in small cups, warm and spoonable.