Bring the water to a rolling boil in a pot. Reduce the heat to low and add the coffee, piloncillo and cinnamon stick. Simmer partially covered for about 10 minutes, stirring occasionally, then turn off the heat and let sit, covered, for 5 minutes.

Strain through a fine sieve or cheesecloth and serve. Alternatively, remove the cinnamon stick and pour the drink into a French press; press down on the plunger and serve.