
Combine butter, brown sugar, white sugar, and cinnamon over medium heat in a large saucepan. Cook 3-4 minutes stirring occasionally.
Add bananas and cook until softened, about 4-5 minutes.
Add in rum and with a long lighter, ignite rum (optional, see note). Allow the flames to burn out (about 30 seconds).
Serve bananas over ice cream and spoon sauce over top.