In a bowl, whisk the masa harina into the water until completely smooth with no lumps. Set aside.
In a medium saucepan over medium heat, warm the milk with the cinnamon stick and piloncillo, stirring until the piloncillo dissolves, about 5 minutes. Don't let it boil.
Whisk the masa mixture again, then slowly pour it into the warm milk while whisking constantly.
Turn the heat to medium-low and simmer, whisking often and scraping the bottom, until thickened to a silky, gravy-like consistency, 6 to 8 minutes.
Add the chopped Mexican chocolate (or cocoa powder plus extra sugar) and whisk until fully melted and smooth, 1 to 2 minutes. Taste and add more piloncillo or brown sugar if you like it sweeter.
Remove from the heat, fish out the cinnamon stick, and stir in the salt and vanilla.
Froth with a molinillo, whisk or milk frother until foamy, then pour into mugs, dust with cinnamon and serve hot.