Soak the chickpeas in water overnight. They will expand to about three times their original size. Drain any excess water from the chickpeas.
Add to blender or food processor, and blend until smooth. Add dates and blend for 2 minutes, gradually adding filtered water to help form a paste.
In a large pot, bring the remaining water to a boil. Add the chickpea paste, vanilla extract, salt, cinnamon, and nutmeg.
Reduce heat and simmer for 20–30 minutes, combining well so all ingredients are properly mixed.
Strain the mixture through a fine-mesh strainer or a clean mesh cloth. Discard the solids and store the liquid chickpea milk in an airtight container. Chill in refrigerator for 2 hours before serving.