Peel the bananas and cut them crosswise into halves. Then slice each half lengthwise, making a total of 8 pieces.

Place a skillet (8- to 10-inch) over low heat. Add butter, brown sugar, cinnamon, and kosher salt. Cook, stirring occasionally, for about 3-4 minutes until the butter melts and fully blends with the sugar, forming a smooth sauce. Initially, the mixture may appear separated but will become smooth as the sugar dissolves.

Add the banana slices and banana liqueur (or vanilla and rum mixture). Gently stir to coat the bananas evenly. Allow to simmer gently, stirring occasionally, for about 1 minute until the bananas soften slightly at the edges. Meanwhile, measure out the 3 tablespoons of dark rum separately; avoid pouring directly from the bottle into the skillet.

Place a long lighter and a skillet lid nearby for safety. Carefully drizzle the measured rum over the bananas without stirring. Immediately use the lighter to ignite the rum (flambé). Gently swirl the skillet to distribute the sauce over the bananas. Allow the flames to extinguish naturally. If flames persist, cover the skillet with the lid to extinguish and remove from heat.

Using a large spoon, transfer bananas and sauce evenly into two serving bowls. Top each serving with vanilla ice cream. Serve right away.