Melt butter and brown sugar together in a skillet over medium heat until caramelized, 3 to 5 minutes. Pour in orange juice; mix well for 2 minutes. Stir in banana slices until evenly coated with orange juice mixture.
Pour rum into the skillet. Light rum carefully using a long match. Shake skillet back and forth until flames die down, about 30 seconds. Cook for 1 minute more.
Divide vanilla ice cream between 2 bowls. Spoon banana mixture over ice cream.
