Preheat oven to 325°F (160°C). Grease a 9-inch springform pan and wrap the outside in foil to prevent leaks.
In a bowl, mix graham cracker crumbs, brown sugar, cinnamon, and melted butter. Press into the bottom of the pan and bake for 10 minutes. Set aside to cool.
In a large bowl, beat cream cheese until smooth. Add sugar and mix until combined.
Beat in eggs one at a time, then add sour cream, vanilla, and mashed bananas. Mix until smooth.
Pour filling over crust. Place the pan in a water bath and bake for 55–65 minutes, until the center is set but slightly jiggly.
Turn off oven, crack door, and let cheesecake cool for 1 hour. Then refrigerate for at least 6 hours or overnight.
Before serving, make the topping: In a skillet, melt butter over medium heat. Add brown sugar and cinnamon; stir until bubbly.
Stir in rum (or extract/water mixture) and carefully add banana slices. Cook 2–3 minutes until soft and glazed.
Spoon warm topping over chilled cheesecake before slicing and serving.