Make the Crust: Preheat your oven to 350°F (175°C). In a bowl, combine graham cracker crumbs and melted butter. Press this mixture into the bottom of a 9-inch springform pan. Bake for 8-10 minutes until golden brown. Set aside to cool.
Prepare the Cheesecake Filling: In a large mixing bowl, beat the softened cream cheese until smooth. Gradually add in the sugar, flour, and vanilla extract, mixing until well combined. Add the eggs one at a time, ensuring each is fully incorporated before adding the next.
Bake the Cheesecake: Pour the cheesecake batter into the cooled crust. Bake in your preheated oven for 50-60 minutes, or until the center is set but still slightly jiggly. Once done, turn off the oven and leave the cheesecake inside for another hour to cool down.
Caramelize the Bananas: In a skillet over medium heat, melt the butter. Add the sliced bananas and brown sugar, cooking for 2-3 minutes per side, or until golden brown. Sprinkle cinnamon over the bananas before removing from heat.
Prepare the Rum Glaze: In a saucepan, combine the rum, brown sugar, and water. Bring to a simmer, cooking for about 2 minutes or until the sauce has thickened slightly.
Assemble the Cheesecake: Once the cheesecake is completely cool, top it with the caramelized bananas and drizzle with the rum glaze. Slice and serve!