In a small saucepan, combine the water and sugar. Heat over medium heat, stirring until the sugar is completely dissolved and a syrup forms.
Allow the sugar syrup to cool to room temperature.
In a medium bowl, whisk together the coconut milk, lime juice, and cooled sugar syrup.
Stir in the shredded coconut for a more intense coconut flavor.
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 shallow container and place it in the freezer. Every 30 minutes, stir with a fork to break up any ice crystals. Repeat this for 3-4 hours.
Before serving, let it sit at room temperature for a few minutes to soften slightly for easier scooping.
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