Pour the coconut milk into a small pot and add the cloves, anise, and cinnamon stick. Heat over medium-high heat until bubbles form around the edges of the pot. Remove from the heat and let cool to room temperature. Strain out the cloves, anise, and cinnamon stick.
In a large pitcher, combine the infused coconut milk, coconut cream, condensed milk, evaporated milk, vanilla extract, and ground cinnamon. Stir in the rum and amaretto. Combine well and refrigerate for at least 2 hours.
Serve chilled in glasses. Garnish with a cinnamon stick if desired.
Notes
The most common type of alcohol used in coquito is rum, but this also includes amaretto, which is an almond liqueur. If you don’t have amaretto and don’t want to make a dash to the store, you can just double the amount of rum. This is an ample but not stupid amount of alcohol; each 8-ounce glass has the equivalent of just about 1 ounce of liquor.