To the jar of a blender, add the milk, ice cream, Mexican chocolate, 1 tablespoon of the cajeta or dulce de leche. Blend until smooth. Crumble two graham crackers into the jar and pulse a few times to combine.
Spread the remaining cajeta or dulce de leche on the remaining graham crackers and sandwich together. Break up into pieces and use for a garnish.
Split the milkshake between two glasses. Spoon a large dollop of whipped cream on top. Top with the graham cracker sandwich pieces and shave some Mexican chocolate on top.