Preheat your oven to 350°F (175°C). In a mixing bowl, combine graham cracker crumbs, melted unsalted butter, and granulated sugar until well mixed. Press this mixture firmly into the bottom of a 9-inch springform pan, ensuring an even layer. Bake the crust for 8-10 minutes until it's slightly golden and fragrant, then remove from the oven and let it cool completely.

Reduce the oven temperature to 325°F (160°C). In a large bowl, beat the cream cheese and sugar together until smooth and creamy, about 2-3 minutes. Gradually add the room-temperature eggs, mixing well after each addition. Stir in the vanilla extract and mashed ripe bananas until fully incorporated. Pour the luscious filling over the cooled crust, smoothing the top with a spatula.

Carefully place the springform pan in the oven and bake the cheesecake for 50-60 minutes. You'll know it's done when the center is set but slightly jiggly. Keep an eye on the edges; they should look firm while the center remains slightly soft. Once baked, remove the cheesecake from the oven and allow it to cool completely at room temperature.

After cooling, cover the cheesecake with plastic wrap and refrigerate it for at least 4 hours, preferably overnight. This chilling step is crucial for the flavors to meld and for the cheesecake to set perfectly, enhancing its smooth and creamy texture.

In a separate bowl, whisk the instant banana pudding mix with cold milk until it thickens, about 2-3 minutes. Spread this delightful pudding layer evenly over the chilled cheesecake. Next, add the fluffy whipped cream, generously spreading it on top.

Slice fresh bananas as a garnish and sprinkle them artfully over the whipped cream. For added texture, top with crushed graham crackers. Slice into wedges and enjoy chilled.