Preheat your oven to 350°F (175°C). In a medium bowl, combine the graham cracker crumbs, melted unsalted butter, and 3 tablespoons of granulated sugar. Press the mixture into the bottom of a 9-inch springform pan. Bake for 8-10 minutes until golden and fragrant, then let cool.

Lower the oven temperature to 325°F (163°C). In a large mixing bowl, beat the cream cheese and 1 cup of granulated sugar until smooth. Add eggs one at a time, then blend in the vanilla and mashed bananas. Pour this mixture over the cooled crust.

Place the filled springform pan in the preheated oven and bake for 50-60 minutes until the edges are set. Turn off the oven and crack the door to cool slowly for an hour, then refrigerate for at least 4 hours (overnight is best).

In a separate bowl, whisk together the instant banana pudding mix and cold milk until thickened. Spread this mixture over the chilled cheesecake, then top with whipped cream, garnishing with fresh banana slices and crushed graham crackers.

Run a knife around the edge of the springform pan before removing the sides. Slice and serve cold, pairing with coffee or tea.