
Add the milk, piloncillo, Mexican chocolate, and cinnamon stick to a medium saucepan or pot. Heat over low-medium heat until the piloncillo and chocolate have completely dissolved. Stir frequently to make sure nothing sticks to the bottom of the saucepan.
Remove and discard the cinnamon stick. You may need to use a strainer if it has broken into pieces.
In a small bowl, whisk together the warm water and masa harina until smooth.
Pour the masa harina mixture into the pot along with the vanilla extract and salt. Whisk to combine.
Bring to a simmer, reduce heat to low, and continue to cook, whisking frequently, for 15-20 minutes until thick, creamy, velvety, and smooth. The champurrado should be thick enough to coat the back of a spoon. For an extra velvety texture, blend the champurrado with an immersion blender to get it super smooth.
Serve and garnish with a touch of ground cinnamon or a cinnamon stick.