Preheat your oven to 350°F (175°C). In a mixing bowl, crush the graham crackers until fine and combine them with melted butter and granulated sugar. Stir until the mixture resembles wet sand, then press this crust mixture firmly into the bottom of a springform pan. Bake for 8 minutes, or until lightly golden, then remove and let it cool completely.

In a large mixing bowl, beat the softened cream cheese with a hand mixer until silky smooth. Gradually incorporate the granulated sugar, mixing well after each addition. Add the eggs one at a time, ensuring each is fully blended before the next. Fold in the sour cream and vanilla extract gently until combined. Pour the creamy cheesecake filling over the cooled crust, smoothing the top.

Lower the oven temperature to 325°F (163°C) and carefully bake the cheesecake for about 55-65 minutes. The edges should be set while the center has a slight jiggle; it will firm up as it cools. Once baked, turn off the oven and allow the cheesecake to cool inside for 1 hour. Then, refrigerate for at least 4 hours, or preferably overnight, to fully set.

In a skillet over medium heat, melt the butter and add brown sugar, stirring until combined. Once bubbling, add ripe banana chunks, cooking for 3-5 minutes, or until they turn golden and sticky. Stir occasionally to coat them evenly in the caramelized mixture. Once done, remove from heat and let them cool while you prepare the rum glaze.

In a small saucepan, combine brown sugar, butter, and dark rum, then cook over medium heat, stirring constantly until blended. Bring the mixture to a gentle simmer and allow it to thicken, about 5-7 minutes. If it isn’t thick enough, create a cornstarch slurry by mixing cornstarch with a little water, then stir it into the glaze until you achieve your desired consistency.

Once the cheesecake is chilled, remove it from the springform pan. Generously top the cheesecake with the caramelized bananas, allowing any excess caramel to drizzle over the edges. Finally, pour the rum glaze on top. For best results, serve your Caramelized Banana Cheesecake warm.