Champurrado is a type of atole, a warm, corn-based beverage commonly served for breakfast in Mexico. Corn, a staple of many Mesoamerican countries, makes its way into all manner of dishes, including warm and cold beverages.
A basic atole is made with water and corn, then heated until it thickens. Champurrado is an elaboration on the original, flavored with spiced chocolate, piloncillo -- a dark, raw cane sugar -- and enriched with milk. Spices such as anise and cinnamon are often added to the beverage, which is stirred with a molinillo, a whisk-like wooden stirrer. Aside from being served at breakfast, champurrado is traditionally served during the upcoming holiday season, namely the day of the dead in November and Christmastime.
Mexican chocolate is commercially sold in tablets, but, should you not find it, bittersweet chocolate is an acceptable substitute. Piloncillo has a deeper, more assertive flavor than dark brown sugar, but if unavailable, it can be substituted with it--all that's needed to mimic the flavor is a tablespoon of molasses.
The idea of drinking the main ingredient in a tortilla, with chocolate and milk no less, may sound a bit odd, but it's a surprisingly well-made match. The corn flavor is definitely detectable, but it adds a nutty, toasty background to the lightly spiced hot chocolate, so drink up!