In a large saucepan over medium heat, combine the brown sugar and butter and heat until the sugar dissolves. Add the sliced bananas and cook until the pieces are browned and slightly softened, about 5 minutes. Remove the pan from the heat, pour in the rum and ignite with a match. Flambe until the flame goes out. Serve the warm mixture over vanilla ice cream with a sprinkling of nuts and a drizzle of the Pineapple-Rum Caramel.
Put the pineapple juice in a medium saucepan over medium heat and simmer until the volume is reduced by half. Once the juice is reduced, add the water and the sugar to the saucepan. Turn the heat down to medium-low and allow the sugar to dissolve. Bring the mixture to a low boil and cook until a light caramel is formed, about 5 minutes. Remove the saucepan from the heat and whisk in the butter, rum, vanilla, and salt. Set the mixture aside until ready to use.
The Pineapple-Rum Caramel can be prepared up to 3 days ahead by refrigerating after making and gently reheating before use.