Rum Eggnog

1 cup coconut milk
1 cup sweetened condensed milk
1 cup evaporated milk
1 cup white rum, or to taste
1 cup water
3 cinnamon sticks
4 egg yolks, well beaten
Ground cinnamon for garnish

Combine all of the milks and the rum in a blender or a food processor. Set aside. Boil the water with the cinnamon sticks. Cool to room temperature. Discard the cinnamon sticks.
Combine all of the ingredients except the ground cinnamon and beat well in a blender or food processor in batches. Pour the eggnog into glass bottles and refrigerate until ready to use. To serve, transfer the eggnog to a punch bowl and sprinkle the cinnamon on top.