Before measuring, shake the cream of coconut and coconut milk cans to ensure the fats are well distributed.
In a blender, combine the puréed pineapple, cream of coconut, coconut milk, white rum, dark rum, lime juice, and ice. Blend the mixture until it becomes smooth and well combined.
Transfer the blender cup to the freezer and allow the mixture to freeze for approximately 20 to 30 minutes until it thickens to a milkshake-like consistency.
Divide the concoction among glasses and adorn each glass with a pineapple wedge and, if preferred, a pineapple leaf.