Peel 4 medium bananas and place bananas on cutting board. Slice each banana in half lengthwise, then slice each long half in half horizontally, creating 4 pieces from each banana. Set aside.
Divide 4 scoops vanilla bean ice cream between serving bowls. Set aside.
Place large flambé pan on stovetop over medium heat. Add ¼ cup unsalted butter, 1 packed cup light brown sugar, and ½ teaspoon ground cinnamon to pan and stir ingredients together as butter melts and brown sugar dissolves.
When butter is almost completely melted, add ¼ cup banana liqueur to pan and stir until ingredients are fully incorporated.
Add quartered bananas to pan. Sauté mixture, stirring and flipping bananas occasionally, 2 to 3 minutes or until bananas begin to soften.
IF USING FIREPLACE LIGHTER: Add ¼ cup dark rum to pan. Stir to incorporate rum, then sauté mixture until sauce begins to bubble. When sauce begins to bubble, ignite lighter then very carefully touch lighter to air around sauce, igniting alcohol vapors.
IF USING STOVETOP FLAME: Lift side of pan closest to you, tilting back of pan down toward stovetop. When back edge of pan is hot, add ¼ cup dark rum to pan, then very carefully tilt pan closer to flame until rum ignites.
After igniting sauce, carefully stir or toss mixture and spoon sauce over banana slices until flames die down and most or all of alcohol has cooked off.
Transfer 4 banana pieces into each bowl of vanilla bean ice cream. Spoon sauce over bananas and ice cream, then serve immediately.