01 - Preheat oven to 350°F. Grease and flour a 9×13-inch baking pan, ensuring even coverage on all surfaces.
02 - In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt until uniformly blended.
03 - In a large mixing bowl, beat the room-temperature butter and granulated sugar with an electric mixer on medium-high speed until pale, light, and fluffy—approximately 3 to 4 minutes.
04 - Add the eggs one at a time, beating well after each addition to ensure full emulsification before adding the next.
05 - Mix in the mashed ripe bananas and pure vanilla extract until evenly distributed throughout the batter.
06 - Gradually add the flour mixture and buttermilk to the wet ingredients in alternating additions, beginning and ending with the flour mixture. Mix until just combined—do not 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. Allow the cake to cool completely in the pan.
08 - In a mixing bowl, whisk together the instant vanilla pudding mix and cold milk for 2 minutes until the mixture thickens to a spreadable consistency.
09 - Spread half of the prepared pudding evenly over the completely cooled cake. Arrange the sliced bananas in a uniform layer on top, then spread the remaining pudding over the bananas to seal.
10 - Refrigerate the assembled cake for at least 30 minutes to allow the pudding layer to firm up properly.
11 - In a chilled bowl, whip the heavy cream, powdered sugar, and vanilla extract with an electric mixer until soft peaks form. Spread or pipe the whipped cream evenly over the chilled pudding layer.
12 - Sprinkle the crushed vanilla wafer cookies over the whipped cream topping just before serving to maintain their crunch. Slice into 12 portions and serve chilled.