Cut bananas in half crosswise; cut each half in half lengthwise. Melt butter in a large skillet over medium-high heat; add brown sugar, and cook, stirring constantly, 2 minutes.
Add bananas to skillet, and remove from heat. Stir in liqueur and rum, and carefully ignite the fumes just above mixture with a long match or long multipurpose lighter.
Let flames die down.
Return skillet to heat, and cook 3 to 4 minutes or until bananas are soft and curl slightly.
Remove from heat.
Serve banana mixture immediately over vanilla ice cream.
