Bring water, piloncillo, cinnamon stick, vanilla, and clove to a boil in a clay or enamel pot over medium-high heat. It should take about 15 minutes for the water to boil and the piloncillo to dissolve.
Remove from heat.
Pour coffee grounds into liquid and mix to combine.
Allow coffee to steep for 10 minutes.
Strain liquid through a cheesecloth-lined sieve into cups or a different pot.