In a medium saucepan, combine the coconut milk, coconut cream, and sugar. Heat over medium heat, stirring until the sugar is completely dissolved. Do not boil.
Remove from heat and stir in the vanilla extract and shredded coconut. Mix well to combine.
Allow the mixture to cool completely to room temperature, then refrigerate for at least 2 hours, or preferably longer, to chill thoroughly.
Pour the chilled ice cream base 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 with a fork to prevent ice crystals from forming.
Place the ice cream in the freezer for at least 4 hours to harden completely.
Before serving, let it sit at room temperature for a few minutes to soften slightly, making it easier to scoop. Sprinkle with extra shredded coconut for garnish.
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