Thoroughly chill your bowls and ingredients.
Puree the pineapple chunks in a blender until smooth.
Pass the blended pineapple through a fine mesh strainer to discard any solids. You should have about a cup of strained puree. (Optionally, leave the fiber in your ice cream for more texture.)
Pour the strained pineapple puree into a saucepan. Then bring it to a boil and simmer over low heat for 15-20 minutes for ¾-1 cup of cooked pineapple puree.
Let it cool for about 30 minutes, then chill it in the fridge so it's as cold as possible before assembling.
Pour the frigid heavy whipping cream into a large chilled bowl and beat with a hand mixer on high for 3-4 minutes until soft peaks form. The peeks shouldn't be too stiff, or the cream will break, and the ice cream could be grainy.
Take out half of the whipped cream and place it in another bowl. Reserve the other half in the freezer while you proceed.
Pour the condensed milk, chilled pineapple puree, coconut cream, vanilla extract, and rum (if using) into the bowl of whipped heavy cream and gently fold to combine.
Then, take the reserved bowl of whipped cream from the freezer and fold in the pineapple coconut cream mixture until combined.
Next, transfer it to a chilled freezer-safe pan and cover with plastic film. Lightly press the plastic film directly on the surface of the mixture, making sure to cover all the angles and edges. Make sure there is no air between the ice cream and the cling film.
Freeze until firm (6 hours to overnight).
Serve in a bowl or cone with your favorite toppings.