Melt the butter in a heavy skillet over a medium-high heat. Add the brown sugar. Stir together and cook for a minute or two. Pour in the cream and stir it around to combine.
Peel the bananas and slice them on the bias inside the peel. Drop the slices into the pan. Next, add the chopped nuts and stir them into the sauce. Then - and this is where you need to be a little careful - stir in the rum. Let it start to bubble, and then carefully use a long lighter to ignite it. (Be sure to have a lid handy in case you need to extinguish the flame.) Let the fire burn and go out (it'll only take about 30 seconds or so), and then stir in the cinnamon at the end. You may also cook the mixture without flambeing it.
Spoon it over a couple of scoops of vanilla ice cream and enjoy immediately.