Add the water to a large pot over medium-low heat. Let it heat for 3-4 minutes. Add the cinnamon stick, star anise, and piloncillo. Stir well and let it simmer for 5 minutes or until the piloncillo is fully dissolved.
Pour in the milk and evaporated milk. Stir well. Immediately add the hot chocolate disk. Bring down the heat to low and stir occasionally.
Add the masa harina and water to the blender. Process everything for 2-3 minutes or until completely smooth. Strain the mixture back into the pot. Don't stop stirring to keep lumps from forming.
Allow the mixture to simmer for 20-25 minutes. Do a taste test and add more piloncillo as needed to sweeten it to taste. Remove the champurrado from the heat and set it aside.
Strain the mixture to remove the spices and any lumps. Let it cool for 10 minutes before serving to let it thicken. Enjoy!
Storage: Refrigerate any leftovers in an airtight container for up to 4 days. The longer you store it, the thicker it gets. Fortunately, you can always thin it down by mixing in 1 tablespoon of milk at a time until it reaches your desired consistency.Reheat: To reheat it, microwave it for up to a minute or until warm. You can also heat it in a small pot over medium-low heat for 8-10 minutes, stirring occasionally.