Preheat your oven to 350°F (175°C) and prepare the crust by mixing crushed graham crackers, melted butter, and granulated sugar. Press into the base of a springform pan and bake for 8 minutes. Cool slightly.

In a large mixing bowl, beat softened cream cheese until smooth, then add granulated sugar, eggs, sour cream, and vanilla extract. Mix until well-combined.

Pour the cheesecake filling onto the cooled crust and bake at 325°F (163°C) for 55-65 minutes. Cool in the oven with the door ajar, then refrigerate for at least 4 hours.

Slice ripe bananas and sauté them in melted butter and brown sugar for about 3-5 minutes until golden. Set aside to cool slightly.

In a saucepan, combine butter, brown sugar, and dark rum, simmer until thickened. Remove from heat and cool slightly.

Once the cheesecake is chilled, top with caramelized bananas and drizzle with the rum glaze before serving.