Bring water, cinnamon stick, clove, and star anise to a boil in a saucepan; remove from heat and allow spices to steep until water is fragrant, about 10 minutes. Strain.

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Heat milk, chocolate, and pinole in another saucepan over medium heat, whisking until chocolate is dissolved and liquid is thickened, about 10 minutes. Remove from heat and add piloncillo; let rest until sugar is dissolved, about 5 minutes more. Pour cinnamon water into chocolate mixture and stir to combine.