01 - Preheat oven to 350°F. Grease and flour a 9x13-inch cake pan, ensuring even coverage to prevent sticking.
02 - In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt until evenly distributed.
03 - In a large bowl, beat the room-temperature butter and granulated sugar together using an electric mixer until the mixture is light and fluffy, approximately 3 minutes.
04 - Add the eggs one at a time, beating well after each addition to ensure full incorporation and a smooth batter.
05 - Mix in the mashed ripe bananas and pure vanilla extract, blending until evenly distributed throughout the batter.
06 - Alternately add the flour mixture and buttermilk to the wet ingredients, beginning and ending with the flour. Mix until just combined, being careful not to overmix.
07 - Pour the batter into the prepared pan and smooth the top with a spatula. Bake for 30 to 35 minutes, or until a toothpick inserted into the center comes out clean. Cool completely in the pan.
08 - In a bowl, whisk together the instant vanilla pudding mix and cold milk for 2 minutes until thickened and smooth.
09 - Spread half of the prepared pudding evenly over the cooled cake. Arrange sliced bananas in a uniform layer on top, then spread the remaining pudding over the bananas.
10 - Refrigerate the assembled cake for at least 30 minutes to allow the pudding layer to set firmly.
11 - While the cake chills, whip the heavy cream, powdered sugar, and vanilla extract together until soft peaks form. Spread or pipe the whipped cream evenly over the pudding layer.
12 - Sprinkle the crushed vanilla wafer cookies over the whipped cream just before serving. Slice into portions and serve chilled for the best flavor and texture.