01 - Preheat oven to 350°F (175°C). Combine graham cracker crumbs, granulated sugar, and melted butter in a mixing bowl. Stir until all crumbs are moistened and the mixture resembles wet sand. Press firmly into the base of a 9-inch springform pan to form an even layer. Bake for 8 minutes until lightly golden, then allow to cool on a rack.
02 - Reduce oven temperature to 325°F (163°C). In a large bowl, beat softened cream cheese until completely smooth, scraping down sides as needed. Add granulated sugar and blend until silky. Incorporate eggs one at a time on low speed, mixing just until combined. Fold in sour cream and vanilla extract, blending gently until no streaks remain.
03 - Pour the filling onto the cooled crust. Tap the pan gently on the counter to eliminate air bubbles. Bake in the preheated oven for 55–65 minutes until edges are set and the center has a slight jiggle. Turn off the oven, crack the door, and let the cheesecake cool inside for 1 hour, then transfer the pan to chill in the refrigerator for at least 4 hours, ideally overnight.
04 - In a skillet over medium heat, melt the unsalted butter. Add brown sugar and stir until dissolved with a bubbling texture. Arrange banana slices in the pan and cook 2–3 minutes per side until deep golden, caramelized, and glossy. Set aside off the heat.
05 - In a small saucepan over medium heat, combine brown sugar, unsalted butter, and dark rum. Stir to combine and simmer gently until sugar dissolves and mixture thickens slightly, about 3–4 minutes. Add vanilla extract. For a thicker glaze, stir in cornstarch mixed with a small amount of water and simmer briefly. Remove from heat and cool slightly before use.
06 - When the cheesecake is fully chilled, carefully arrange caramelized bananas over the surface. Drizzle warm rum glaze generously across the top, allowing some to drip down the sides. Slice with a clean, sharp knife and serve while the glaze remains slightly warm.