Add the coffee, cocoa, star anise, cinnamon and cardamom to a jar and cover with the water. Shake lightly and cover with plastic wrap. I like to wrap a rubber band around the top to secure.
Poke a few holes in the top.
Refrigerate 12-24 hours.
Strain through fine mesh strainer lined with cheesecloth twice and store in an airtight container in the fridge for up to a week.
To serve, mix with equal parts water and serve hot or over ice — add more or less water depending on how strong you like your coffee.