Melt the butter in a large skillet over medium heat.

Stir in the brown sugar and cinnamon, and cook 2 minutes, stirring constantly, until it becomes a smooth, bubbling caramel.

Lay the banana pieces cut-side down in the caramel and cook 2 minutes, until they soften and the edges turn golden.

Carefully flip and cook 1 minute more on the other side.

Remove the skillet from the heat, pour in the rum and banana liqueur if using, then return to the heat.

Tilt the pan to let the alcohol catch the flame if cooking on gas, standing back with a lid nearby, or simply simmer 1 to 2 minutes until the alcohol smell mellows and the sauce thickens and coats the back of a spoon.

Spoon the warm bananas and sauce immediately over scoops of vanilla ice cream, and serve right away.