Preheat your oven to 350°F (175°C). In a food processor, crush graham crackers until fine crumbs form. In a bowl, mix the crumbs with melted unsalted butter and granulated sugar until well combined. Press this mixture firmly into the bottom of a springform pan, creating an even base. Bake for 8 minutes, then set aside to cool completely.

In a large mixing bowl, beat softened cream cheese using an electric mixer until smooth and creamy. Gradually add granulated sugar, mixing until well incorporated. Add eggs one at a time, beating well after each addition. Finally, fold in sour cream and vanilla extract until the mixture is lump-free.

Pour the cheesecake filling over the cooled crust, smoothing out the top with a spatula. Tap the pan gently on the counter to release any air bubbles trapped in the filling. Place it in the oven and bake at 325°F (163°C) for 55-65 minutes.

After baking, turn off the oven and crack the door open. Allow the cheesecake to cool in the oven for 1 hour, then transfer it to the refrigerator and chill for at least 4 hours, preferably overnight.

To prepare the topping, slice ripe bananas into ½-inch pieces. In a skillet over medium heat, melt unsalted butter and add brown sugar. Stir until the sugar dissolves, then add the banana slices. Cook gently for 3-5 minutes until they are golden and caramelized.

In a small saucepan, combine brown sugar, remaining butter, and dark rum. Heat over medium heat, stirring until the sugar dissolves. Bring to a simmer for about 3-5 minutes until the mixture thickens slightly.

Once your cheesecake has chilled and is set, remove it from the springform pan. Arrange the warm caramelized bananas on top, drizzle the rum glaze over the bananas and cheesecake, slice, and serve immediately.