01 - Preheat oven to 325°F (163°C). Mix graham cracker crumbs, brown sugar, and melted butter in a bowl. Press evenly into the base of a 9-inch springform pan. Bake for 10 minutes, then let cool completely.
02 - Beat cream cheese until smooth using an electric mixer. Gradually add granulated sugar, mixing until incorporated. Add eggs one at a time, beating briefly after each addition. Stir in sour cream, vanilla extract, mashed bananas, and flour just until combined. Do not overmix.
03 - Pour the filling over the cooled crust. Place the filled springform pan inside a larger pan and fill the outer pan with hot water to create a water bath. Bake for 60 to 70 minutes, or until the center is just set. Turn off oven, crack oven door, and let cheesecake cool in oven for 1 hour. Remove from oven and refrigerate for at least 4 hours or overnight.
04 - Melt butter in a skillet over medium heat. Add brown sugar, cinnamon, and salt; stir until bubbly. Add sliced bananas and cook for 2 to 3 minutes until softened. Pour in rum and simmer for 1 minute, allowing the glaze to thicken. Remove from heat and cool slightly.
05 - Remove chilled cheesecake from the springform pan. Spoon caramelized banana topping over the surface, letting the rum glaze gently cascade over the edges. Slice and serve immediately.