Preheat the oven to 325°F.

In a medium bowl, combine graham cracker crumbs, melted butter, and sugar. Press the mixture firmly into the bottom of a 9-inch springform pan to form the crust.

Bake for 10 minutes, then remove and let cool.

In a large mixing bowl, beat the softened cream cheese and sugar together until smooth and creamy. Add the vanilla extract and mix well.

Add the eggs one at a time, mixing on low speed until just combined. Pour the cream cheese mixture over the cooled crust.

In a skillet over medium heat, melt 2 tablespoons of butter. Add the sliced bananas and brown sugar, cooking for about 3-4 minutes until the bananas are caramelized.

Remove from heat and gently fold the caramelized bananas into the cheesecake batter.

Pour the cheesecake mixture into the springform pan and smooth the top.

Bake for 55-60 minutes, or until the center is set but still slightly jiggly.

Turn off the oven and let the cheesecake cool in the oven with the door slightly ajar for 1 hour.

Remove from the oven and refrigerate for at least 4 hours, preferably overnight.

For the rum glaze, combine dark rum, cornstarch, and lemon juice in a small saucepan over medium heat. Stir until the mixture thickens, about 3-5 minutes.

Let it cool slightly before drizzling over the chilled cheesecake.

Slice and serve the cheesecake chilled, drizzled with the rum glaze.