In a saucepan, combine the coconut milk, heavy cream, and sugar. Heat over medium heat until the sugar is completely dissolved, stirring constantly. Do not boil.
Stir in the shredded coconut and vanilla extract. Let the mixture sit for 10 minutes to allow the coconut flavor to infuse fully.
Allow the mixture to cool completely to room temperature. Then, strain it through a fine-mesh sieve to ensure a smoother ice cream texture.
Pour the mixture into an ice cream maker and churn according to the manufacturer's instructions. If you don't have an ice cream maker, pour the mixture into a freezer-safe container and stir it every hour during the freezing process.
Freeze for at least 4 hours, or until firm enough to scoop. Before serving, let it sit at room temperature for a few minutes to soften slightly.
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