In a large saucepan, bring the water, cinnamon sticks, and piloncillo to a simmer over medium heat. Stir occasionally until the piloncillo has completely dissolved, about 10 minutes.
In a separate bowl, whisk the masa harina with 1 cup of the milk until smooth and completely free of lumps.
Gradually pour the masa harina mixture into the saucepan with the piloncillo syrup, stirring constantly.
Add the remaining 3 cups of milk and the chopped Mexican chocolate to the saucepan.
Reduce the heat to medium-low and simmer, stirring frequently to prevent the bottom from burning, until the chocolate is melted and the champurrado thickens, about 10 minutes.
Remove from heat, carefully discard the cinnamon sticks, and serve hot.
Notes
For a richer flavor, you can substitute the water with additional milk. Ensure the masa harina is completely dissolved before adding it to the hot liquid to avoid lumps.