Preheat oven to 350°F (175°C). In a bowl, combine graham cracker crumbs, melted butter, and sugar. Press the mixture into the bottom of a 9-inch springform pan. Bake for 8-10 minutes, or until golden brown.
Make the Cheesecake:
In a large bowl, beat cream cheese until smooth. Gradually add sugar, flour, and vanilla extract, beating until well combined. Beat in eggs one at a time until just combined.
Bake the Cheesecake:
Pour cheesecake batter into the prepared crust. Bake for 50-60 minutes, or until the center is set but still slightly jiggly. Turn off the oven and leave the cheesecake inside for another hour to cool.
Caramelize the Bananas:
In a skillet, melt butter over medium heat. Add sliced bananas and brown sugar. Cook for 2-3 minutes per side, or until golden brown. Sprinkle with cinnamon.
Make the Rum Glaze:
In a saucepan, combine rum, brown sugar, and water. Bring to a simmer and cook for 2 minutes, or until the sauce has thickened.
Assemble:
Once the cheesecake is completely cool, top with caramelized bananas. Drizzle with rum glaze and serve immediately.