Melt the butter in a large skillet over medium heat. Add the brown sugar, cinnamon, and nutmeg, and cook, stirring, until the sugar dissolves, about 2 minutes. Add the bananas and banana liqueur and cook on both sides until the bananas start to soften and brown, about 3 minutes. Carefully add the rum and shake the pan back and forth to warm the rum and flame the pan. (Or, off the heat, carefully ignite the pan with a match.) Shake the pan back and forth, basting the bananas, until the flame dies.
Divide the ice cream among 4 dessert plates. Gently lift the bananas from the pan and place 2 halves on the ice cream. Spoon the sauce over the ice cream and serve immediately.