In a small saucepan, combine the water and sugar. Heat over medium heat, stirring until the sugar is completely dissolved. This will be your simple syrup.
Allow the simple syrup to cool to room temperature.
Peel and cube the pineapple, then puree it in a blender until smooth.
In a large bowl, combine the coconut milk, cooled simple syrup, pineapple puree, and freshly squeezed lime juice.
Add the shredded coconut to enhance the coconut flavor and texture of the ice cream.
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 dish and place it in the freezer. Every 30 minutes, stir it with a fork to prevent large ice crystals from forming. Repeat this for 3-4 hours.
Before serving, let it sit at room temperature for a few minutes to soften for easier scooping.
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