Preheat the oven to 325°F and grease a 9-inch springform pan.

In a mixing bowl, combine graham cracker crumbs, melted butter, and granulated sugar. Press the mixture into the bottom of the prepared springform pan to form the crust. Bake for 10 minutes and let cool.

In a large bowl, beat the softened cream cheese and granulated sugar until smooth. Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract, mashed bananas, and lemon juice until fully combined.

Pour the cheesecake filling over the cooled crust. Bake for 50-60 minutes, or until the center is set and slightly jiggly. Turn off the oven and leave the cheesecake inside for 1 hour. Remove from the oven and let cool to room temperature, then refrigerate for at least 4 hours or overnight.

In a skillet over medium heat, melt the butter. Add the sliced bananas and brown sugar, cooking until caramelized, about 3-4 minutes. Stir in the dark rum and cook for an additional minute. Remove from heat and let cool slightly.

Once the cheesecake is chilled, top it with the caramelized bananas.

For the rum glaze, whisk together powdered sugar, dark rum, and milk in a small bowl until smooth. Drizzle the glaze over the cheesecake before serving.