Step 1In a 2-gallon stock pot, bring 2 quarts of water and the cinnamon sticks to a boil over high heat.
Step 2Meanwhile, in a blender, combine half of the masa with 1 quart water to form a slurry (the blender should be three-fourths full). Add the rest of the masa to the slurry and blend to combine. Add the masa slurry in a thin, steady stream to the cinnamon water and stir to combine, still over high heat.
Step 3Add the chocolate pieces to the blender, along with the evaporated and condensed milks. Blend the chocolate mixture completely, then slowly stir it into the stock pot. Stir in the milk.
Step 4Continue to cook until the mixture comes to a gentle boil, stirring constantly. Adjust the consistency by whisking in additional masa as desired, gently boiling the mixture a few minutes to allow the masa to cook and thicken. Adjust sweetness as desired with sugar.
Step 5Remove the champurrado from the heat and strain to remove the cinnamon sticks. Serve immediately, or cool and refrigerate until needed. It will keep for 3 days refrigerated.