Heat the water, butter, and sugar in a pan over high heat until it begins to boil.
Turn the heat down to low and add the flour and cacao powder. Stir well until no flour clumps remain.
Add the egg and vanilla and mix with a hand mixer or really with with a spatula to incorporate.
Fill a piping bag fitted with a large star tip with the churro dough and pipe long pieces of dough onto a baking sheet.
Cut the ends of the churro dough with kitchen scissors so each one has a clean cut end. Bake in the oven until crispy on the outside.
In a shallow bowl, mix together the cinnamon, sugar, and cocoa with a spoon until well mixed.
While the churros are still warm, place each one in the bowl with the cinnamon mixture and toss to coat.