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.
Use caution when igniting the run in step 2. Use a long match such as a fireplace match or long barbeque lighter. Ignite the fumes at the edge of the pan, not the liquid itself. Do not lean over the skillet as you ignite the fumes.
Per Serving: 300 calories;13.3 g fat;
41 g carbohydrates;
3.3 g protein;
44 mg cholesterol;
97 mg sodium.