01 - Preheat oven to 350°F. Grease and flour a 9x13-inch cake pan.
02 - In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
03 - In a large bowl, use an electric mixer to beat the butter and sugar together until light and fluffy, about 3 minutes. Add the eggs one at a time, beating well after each addition.
04 - Mix in the mashed bananas and vanilla extract until evenly combined.
05 - Alternately add the flour mixture and buttermilk to the butter mixture, beginning and ending with the flour. Mix until just combined; do not overmix.
06 - Pour the batter into the prepared pan and smooth the top evenly. Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean. Cool completely in the pan.
07 - In a bowl, whisk together the instant vanilla pudding mix and cold milk for 2 minutes until thickened.
08 - Spread half of the pudding evenly over the cooled cake. Arrange the sliced bananas in a single layer on top, then spread the remaining pudding over the bananas.
09 - Refrigerate the assembled cake for at least 30 minutes to allow the pudding layer to set firmly.
10 - In a chilled bowl, whip the heavy cream, powdered sugar, and vanilla extract with an electric mixer until soft peaks form.
11 - Spread or pipe the whipped cream over the pudding layer. Sprinkle with crushed vanilla wafer cookies just before serving.