In a large saucepan, add masa and set over medium heat. Immediately add water in a slow, thin stream while whisking constantly to avoid lumps. Bring to a simmer and whisk in milk, chocolate, brown sugar, and a generous pinch of salt until chocolate is melted, about 1 minute. Add cinnamon.
Return to a simmer and lower heat to low. Continue to simmer gently, whisking constantly, for 5 minutes. Discard cinnamon stick, if using. Thin with additional water, as needed, to create a thick-yet-drinkable hot beverage (the exact consistency is a matter of personal taste), reheating as necessary. Taste, adding more sugar or salt if desired.
Froth with a whisk or immersion blender, then ladle into mugs, and serve.
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