Preheat the oven to 350°F (175°C).
Combine graham cracker crumbs, 1/3 cup sugar, and melted butter in a bowl; mix well. Press mixture into the bottom of a 9-inch springform pan.
Bake crust for 10 minutes. Let cool while preparing filling.
In a large bowl, beat cream cheese and 1 1/2 cups sugar until smooth. Add mashed banana and blend well.
Beat in eggs, one at a time. Mix in heavy cream and flour until just combined.
Pour filling over crust. Bake for 60-70 minutes, until center is set.
Cool to room temperature, then refrigerate for at least 4 hours or overnight.
Whisk pudding mix and milk together until thickened. Fold in whipped topping.
Spread pudding mixture over chilled cheesecake. Garnish with banana slices before serving.