Add all ingredients to a medium sauce pan and warm, over medium heat, until the coconut milk solids and the honey have completely dissolved in the juice. (Do not bring to a boil.)
Remove from the heat and pour the mixture into a bowl. Chill in the refrigerator, stirring occasionally so that the pomegranate juice and coconut milk don’t separate. You’ll want to chill the mixture (about an hour or so) until it’s cool enough to churn but not so cold that the coconut milk starts to solidify again.
Churn in an ice cream maker according to your manufacturer’s instructions.
Freeze 4-6 hours before eating.
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