1. In a dry pan over medium heat, toast the masa harina for a few minutes until fragrant, stirring constantly.
2. In a pot, heat water and milk (if using) over medium heat and add the cinnamon stick.
3. Add the piloncillo or brown sugar to the pot and stir until completely dissolved.
4. Break the Mexican chocolate tablets into pieces and add them to the pot, stirring until melted.
5. In a separate bowl, whisk the toasted masa harina with a small amount of warm water until smooth to avoid lumps.
6. Slowly pour the masa mixture into the pot, whisking constantly to combine.
7. Continue cooking over low-medium heat, stirring frequently to prevent burning, for about 15-20 minutes until the mixture thickens.
8. Optionally, add vanilla extract or other spices like cloves or anise for extra flavor.
9. Use an immersion blender or a molinillo to froth the champurrado before serving.
10. Serve hot with Mexican pastries like conchas or buñuelos for an authentic experience.
11. Store leftovers in the refrigerator and reheat with extra liquid if needed before serving again.