Preheat the oven to 325°F (163°C). Line a 9x13 pan with parchment paper, leaving an overhang for easy removal later. Lightly grease the parchment if it’s sticky.

Mix crushed cookies, melted butter, and sugar until evenly moistened. Press the mixture into the bottom of the pan in an even layer. Bake for 8–10 minutes until set and lightly golden. Let it cool while you prepare the cheesecake layer.

Beat the softened cream cheese on medium speed until smooth and lump-free. Add sugar and mix until creamy. Scrape the sides down so everything blends evenly. Add eggs one at a time, mixing just until incorporated. Blend in vanilla and sour cream (or Greek yogurt) until smooth.

Pour half of the cheesecake batter over the cooled crust and spread gently. Spoon or dollop half of the prepared vanilla pudding over the cheesecake layer and spread lightly. Arrange a single layer of thin banana slices over the pudding. Gently pour the remaining cheesecake batter over the bananas and smooth the top.

Add the rest of the pudding in spoonfuls across the top and use a knife to make soft swirls. Bake at 325°F for 28–35 minutes until the edges are set but the center still has a slight jiggle. Let it cool on a rack for about an hour, then refrigerate for at least 4 hours — overnight is best.

Before serving, fold whipped topping until fluffy and spread over the top. Garnish with crushed cookies and a few banana slices. Use the parchment overhang to lift the slab from the pan onto a cutting board. Cut into squares and serve chilled.