Step 1: In a large saucepan, combine 2 cups of the milk and 2 cups of water. Add the broken Mexican chocolate pieces. Heat over medium-low heat, stirring occasionally, until the chocolate is fully melted and smoothly incorporated into the liquid.
Step 2: In a separate bowl, whisk together the masa harina with the remaining 2 cups of milk until a smooth, lump-free mixture forms. Ensure there are no dry pockets of masa.
Step 3: Once the chocolate is melted in the saucepan, add the piloncillo (or dark brown sugar), cinnamon stick, and star anise (if using). Stir continuously until the piloncillo is completely dissolved, about 5-7 minutes.
Step 4: Slowly pour the masa harina and milk mixture into the saucepan with the chocolate liquid, whisking constantly to prevent any lumps from forming. This is key to a smooth champurrado.
Step 5: Continue to cook the champurrado over medium-low heat, stirring frequently with a whisk or molinillo, for about 15-20 minutes. The mixture will gradually thicken to a rich, creamy consistency that coats the back of a spoon. Be sure to scrape the bottom to prevent sticking.
Step 6: Once thickened to your desired consistency, remove the cinnamon stick and star anise. If using, stir in the vanilla extract.
Step 7: For an extra frothy texture, carefully blend a portion of the hot champurrado in a blender for 30-60 seconds, or use a molinillo directly in the pot. Serve immediately in mugs.
Step 8: Garnish with a sprinkle of ground cinnamon, if desired, and enjoy your delicious homemade Champurrado recipe!