Preheat oven to 350F degrees.
Grind the cookies in a food processor until they are crumbs. Then add the sugar and melted butter and mix well.
Grease a 7-inch cheesecake pan. Press the crumb mixture on the bottom and part the way up the sides of the pan.
Put the pan in the heated oven for 8-10 minutes. Then remove and set aside to cool down.
In a large bowl beat cream cheese, sugar, flour, and pudding mix with an electric mixer on low speed until fully blended.
Add sour cream, mashed bananas, and vanilla extract. Mix well. It will be a little lumpy and that is ok.
Add eggs and mix slowly until fully blended. You want the eggs to be well blended with the mixture but be careful not to add a lot of air to the mix.
Pour the cheesecake batter onto the crust.
Bake for 1.5 hours at 300 in a water bath. You can either set the pan in foil before placing it in the water bath or you can use a Bath Cheesecake Wrap. Turn off the oven and leave the door closed for 30 minutes. The cheesecake will continue to cook but will also start to cool slowly.
Remove from oven and allow to cool on the counter before placing the completely cooled cheesecake in the refrigerator.
Before serving arrange a single layer of banana slices on top of the cheesecake. Then garnish with whipped cream, sliced bananas, and cookies or vanilla wafers.