Melt butter in a medium skillet over medium heat. Add brown sugar, cinnamon, and a pinch of salt. Stir constantly 2 to 3 minutes until smooth and bubbling.
Lay banana slices in the sauce. Cook 1 to 2 minutes per side, spooning sauce over the top, until softened but still holding their shape.
Remove skillet from heat. Add dark rum. Return to heat and carefully ignite with a long match or lighter. Allow flames to burn off naturally, about 30 to 60 seconds.
Once flames subside, stir in vanilla extract if using.
Place a scoop of vanilla ice cream in each bowl. Spoon bananas and sauce over the top. Serve immediately.