In a medium saucepan over medium heat, add the pineapple juice and brown sugar.
Bring to a gentle simmer, stirring, until the brown sugar is completely dissolved.
Add in the butter, cinnamon, and a pinch of salt. Continue cooking at a gentle bubble, stirring occasionally, until it's reduced and thickened, about 5 minutes.
Stir in the rum and cook for 1 more minute.
Remove from the heat.
Spoon over grilled pineapple and a scoop of vanilla ice cream!
