Important: Chill your bowls and ingredients in the refrigerator before starting.
Peel and chop pineapple, then puree it in the blender until smooth.
Pass the blended pineapple through a fine mesh strainer to discard any solids for smoother ice cream. You should end up with about 2 cups of strained puree. (Skip this step if you don't mind pineapple fiber in your ice cream.)
Pour the strained pineapple puree into a saucepan. Then, bring it to a boil and simmer over low heat for 20-25 minutes. You should have about (1-1½ cups of cooked pineapple puree).
Let it cool for about 30 minutes, then transfer it to the fridge to completely chill.
Pour the very cold, heavy whipping cream into a large chilled metal or glass bowl. Whisk 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 will 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, lemon juice, vanilla extract, and rum (if using) into the bowl of whipped heavy cream and gently fold to combine.
Add this to the reserved bowl of whipped cream and gently fold to combine.
Next, transfer the mixture to a chilled freezer-safe pan and cover with plastic film. Lightly press the plastic film directly on the surface, covering all the angles and edges. Make sure the cling wrap touches the ice cream's surface so there's no space between the ice cream and the cling film. (That keeps ice crystals from forming.)
Freeze until firm (6 hours or overnight).
Take the ice cream out of the freezer 5-10 minutes before scooping and serving in a bowl or cone with your favorite toppings.