Cut bananas in half lengthwise; cut each half crosswise to make 12 pieces. Combine apple juice and apple pie spice in a large skillet. Add banana pieces to juice mixture; cook over medium heat just until banana is heated, basting often with juice mixture.
Combine cornstarch, rum, and flavorings, stirring until smooth; add to banana mixture. Bring to a boil; cook, stirring constantly, 1 minute.
To serve, spoon 1/2 cup ice cream into each of 6 dishes. Spoon banana mixture evenly over ice cream, and serve immediately.
Tip: If you don't want to use rum, add an extra 2 tablespoons of apple juice.