Add the sugar, key lime juice, and water together in a saucepan and heat, mixing well, until the sugar dissolves.
Add the kiwi, plus half the key lime syrup and the coconut milk together in a blender. Blend until the kiwi is liquefied. Optionally run the mixture through a strainer to remove the seeds (I left them). Test the sorbet for sweetness and add more syrup as needed. Remember, it should taste a lot sweeter at room temperature as the sweetness is subdued when frozen. (I ended up using all the syrup)
Chill the sorbet in the refrigerator for at least an hour or two.
Churn according to the manufacturer instructions on your ice cream maker. Alternatively, you can use these instructionsto make the sorbet without and ice cream maker.
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