Prepare the Tamarind. Remove the outer shell from the tamarind pods and as many fibrous strings as possible. Note: It’s easiest to pull the fibers from one end downwards along the length of the pod.
Bring 4 cups of water to a boil in a large pot. Add the peeled tamarind pods to the boiling water. Reduce the heat to medium-low and simmer for 10 minutes.
Turn off the heat and let the mixture cool to room temperature, about 1 hour.
Once cooled, separate the sticky tamarind paste from the seeds in the pot. Discard the hard seeds and any remaining fibrous strings.
Transfer the tamarind mixture to a blender. Add 1/2 cup of the grated piloncillo and blend on high until smooth. Taste and add the remaining piloncillo if desired.
Work the tamarind mixture through a mesh strainer into a pitcher or large jar.
Mix in the remaining 8 cups of water (or to your liking). Chill for a few hours or serve immediately over ice.