Melt 2 tablespoons of butter in a large nonstick skillet over medium-high heat. Place the bananas in the butter, cut side down. Pour the sugar around the bananas and let it cook until it starts to caramelize, moving the bananas around a bit to ensure even browning.
Remove the skillet from heat; add in the rum, and orange juice. Return the skillet to heat and let reduce for a minute. Turn the bananas and let the juices reduce for another minute.
Remove the skillet from heat and swirl in the remaining tablespoon of butter.
Serve the bananas in shallow bowls drizzled with the caramel pan sauce. Top with orange segments and a scoop of vanilla ice cream. Garnish with a sprig of mint.