In a large pot boil the quart of water, brown sugar, cinnamon (and anise star, if using) over medium heat, until the sugar has dissolved.
Add the milk and Mexican chocolate to the pot. Stir constantly until the chocolate has completely melted and blended with the rest of the ingredients.
Dissolve the Masa harina in the 1 cup of water and stir until the mix is no longer chunky.
Add the dissolved masa harina to the pot, stirring constantly so no lumps form while it all cooks. Cook for 15 minutes over low heat, stirring often, until the Champurrado is thick and creamy.
Remove and discard the cinnamon stick and the anise star seed (if you used it). Serve warm, enjoy!