For the Caribbean coconut ice cream, heat the coconut milk together with all other ingredients in a saucepan at low temperature, but do not bring to a simmer.
Keep stirring until the liquid has thickened somewhat. Remove from heat and allow to cool.
Pour ice cream mixture into a large bowl and place in the freezer for about 3 hours.
After 3 hours, stir the already frozen ice cream vigorously with a large whisk and place back in the freezer for 1 to 2 hours. Then stir again and return to the freezer.
Repeat this process until the Caribbean coconut ice cream has reached the desired consistency.