Combine butter, sugar, and cinnamon in a large sauté pan. Place pan over low heat and cook, stirring, until sugar dissolves. Stir in banana liqueur, then place bananas in pan. When bananas soften and begin to brown, carefully add rum. Continue to cook sauce until rum is hot, then tip pan slightly to igniter rum. When flames subside, lift bananas out of pan and place four pieces over each portion of ice cream. Generously spoon warm sauce over ice cream and serve immediately.