Preheat your oven to 350°F (175°C). In a mixing bowl, combine the graham cracker crumbs, granulated sugar, and melted butter. Press into the bottom of a 9-inch springform pan to form a crust. Bake for 10 minutes, then let it cool completely.
In a large mixing bowl, beat 8 ounces of softened cream cheese with 1 teaspoon of vanilla extract until smooth. Gradually add in the vanilla pudding mix, mixing until well combined. In another bowl, whip 1 ½ cups of heavy cream until stiff peaks form. Gently fold the whipped cream into the cream cheese mixture until fully incorporated.
Slice the 3 to 4 medium bananas into thin rounds. Spread a layer of the cream cheese filling over the cooled crust, followed by a layer of sliced bananas. Repeat the layers, finishing with the remaining cream cheese filling on top.
In a clean mixing bowl, beat the remaining 1 ½ cups of heavy cream with the ½ cup of powdered sugar and 1 teaspoon of vanilla extract until stiff peaks form. Spread the whipped cream topping over the cheesecake.
Cover the cheesecake with plastic wrap and refrigerate for at least 4 hours, or overnight.