In a blender, combine dairy or nondairy milk, sweetened condensed milk, unsweetened cocoa powder, ground cinnamon, vanilla extract, unsweetened coconut milk, and sweetened condensed coconut milk. Blend until very frothy, about 1 minute. Refrigerate until cold, 4 to 6 hours. Whisk before serving. Divide among six glasses, and garnish with more cinnamon.
