Pour the carrot juice into an ice cube tray and freeze until solid, at least 2 hours.
Put the pineapple, buttermilk, dates, carrot juice ice cubes and cinnamon into a blender. Blend on high until smooth, turning off the blender and pushing down on the ingredients with a spatula or wooden spoon as needed to help the blending process. Add 1 to 2 tablespoons of cold water if needed to adjust consistency.
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