Preheat your oven to 350°F (175°C). In a mixing bowl, crush the graham crackers into fine crumbs, then combine them with melted butter and granulated sugar until well mixed. Press this mixture firmly into the bottom of a springform pan to create an even layer. Bake for 8 minutes until slightly golden, then set aside to cool.

In a large mixing bowl, beat the softened cream cheese using an electric mixer until smooth and creamy. Gradually add granulated sugar, mixing until fully incorporated. Add the eggs one at a time, ensuring each is well blended before adding the next. Finally, fold in the sour cream and vanilla extract gently until silky and smooth.

Pour the cheesecake batter over the cooled crust in the springform pan. Bake in the preheated oven at 325°F (163°C) for 55–65 minutes until edges are set and center remains slightly jiggly. Cool slowly in the oven with the door open for about 1 hour, then refrigerate for at least 4 hours.

Slice the ripe bananas into thick rounds. In a skillet over medium heat, melt butter and add brown sugar. Stir until sugar dissolves and bubbles form. Add banana slices to the skillet and cook for 2-3 minutes per side until golden and caramelized.

In a saucepan, combine brown sugar, butter, and dark rum. Heat over medium-low, stirring occasionally until the mixture simmers and thickens slightly. Incorporate cornstarch slurry if desired, cooking for an additional 1-2 minutes.

Once the cheesecake has chilled, remove it from the springform pan and place on a serving plate. Top generously with caramelized banana slices and drizzle warm rum glaze over the top.