Place fresh pineapple in the blender and blend until not quite smooth. (I liked the little bits of pineapple in the ice cream.) In a mixing bowl, whisk together the milk, 1 3/4 cups of the pineapple puree, sugar, salt, and rum. Pour into the ice cream machine and freeze according to manufacturer's directions.
While the ice cream is churning, preheat oven to 350 degrees. Spread 1 cup of coconut across a baking sheet. Toast in the oven until lightly browned, about 6-7 minutes. Remove from the oven and let cool.
When the machine is finished, stir in about 3/4 cup of the coconut and place in freezer. Freeze until as firm as desired. Serve with the extra coconut sprinkled on top, along with chunks of pineapple, if desired. Enjoy!
There aren't a lot of recipes that I am brand specific for the ingredients, but Thai coconut milk is hands down the best I've tried. I recommend it for any and all ice cream recipes.