Preheat the oven to 350°F (175°C). In a bowl, combine crushed graham crackers, melted unsalted butter, and granulated sugar. Press into the bottom of a 9-inch springform pan. Bake for 8 minutes and cool.

In a large mixing bowl, beat cream cheese until smooth. Gradually add granulated sugar. Add eggs one at a time, mixing well. Fold in sour cream and vanilla extract. Pour over the cooled crust.

Lower the oven temperature to 325°F (163°C) and bake the cheesecake for 55-65 minutes until edges are set but the center jiggles. Cool in the oven for 1 hour and refrigerate for at least 4 hours.

In a skillet, melt 2 tablespoons of butter. Stir in the brown sugar until dissolved. Add sliced bananas and sauté for 3-5 minutes until caramelized. Remove from heat to cool slightly.

In the same skillet, melt another tablespoon of butter. Stir in brown sugar and dark rum. Simmer for 5-7 minutes until thickened. Mix in cornstarch slurry for extra thickness, if desired.

Once the cheesecake has chilled and set, release it from the pan, top with warm caramelized bananas, and drizzle with rum glaze. Slice and serve.