Whisk the chocolate, cocoa powder, sugar, and cinnamon together in a large saucepan. Add the milk and bring to a simmer over medium heat, whisking occasionally, until hot and smooth, about 5 minutes. Stir in the salt.
Remove from the heat and add the wine. Divide among 8 small glasses or mugs, garnish with a cinnamon stick and a dusting of cocoa powder, if desired, and serve.