In a medium saucepan, combine the coconut milk, heavy cream, honey, and sugar. Heat over low heat, stirring until the sugar is completely dissolved.
Zest the lime, then juice it. Add a pinch of salt and the vanilla extract to the milk mixture.
Let the mixture cool completely, then refrigerate for at least 2 hours to allow the flavors to meld.
Pour the chilled mixture into an ice cream maker and churn according to the manufacturer's instructions until creamy.
If you don't have an ice cream maker, pour the mixture into a shallow dish and place it in the freezer. Every 30 minutes, stir it to prevent ice crystals from forming.
Once the ice cream is completely solidified (after about 4-5 hours of freezing), serve garnished with fresh lime wedges or shredded coconut.
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