Preheat oven to 350°F (175°C). Line an 8x8-inch pan with parchment paper. In a bowl, mix crushed vanilla wafers, sugar, and melted butter. Press the mixture into the pan and bake for 8-10 minutes, until golden. Let cool.
Beat softened cream cheese and sugar until smooth. Add eggs, one at a time, then stir in vanilla and sour cream. Pour the mixture over the cooled crust and spread evenly.
Whisk together cold milk and pudding mix until thickened, about 2 minutes. Layer sliced bananas over the cheesecake, then spread the pudding mixture on top.
Bake for 30-35 minutes, until the center is set and edges are golden. Cool to room temperature, then refrigerate for at least 2 hours.
Top with whipped cream, crushed vanilla wafers, and a caramel drizzle. Cut into squares and serve!