Peel the pineapple, cut it into smaller pieces, and purée until smooth in a blender.
In a large bowl, combine the coconut milk, heavy cream, honey, vanilla extract, and pineapple purée. Mix well until you have a homogeneous mixture.
Add the white rum and shredded coconut, then mix again. The rum helps to keep the ice cream soft.
Pour the mixture into an ice cream maker and process according to the manufacturer's instructions until creamy.
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 prevent ice crystals from forming.
Once the ice cream has reached the desired consistency (after about 4-5 hours of freezing), serve sprinkled with shredded coconut and garnished with fresh pineapple pieces, if desired.
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