01 - Preheat oven to 350°F. Grease and flour two 9-inch round cake pans.
02 - In a bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Set aside.
03 - In a large mixing bowl, beat the butter and granulated sugar together until light and fluffy. Add the eggs one at a time, mixing well after each addition, then stir in the vanilla extract.
04 - Mix in the mashed bananas until evenly distributed. Alternately add the flour mixture and buttermilk in three additions, beginning and ending with the flour. Stir until just combined; do not overmix.
05 - Divide the batter evenly between the two prepared cake pans and smooth the tops. Bake for 28 to 32 minutes, or until a toothpick inserted in the center comes out clean.
06 - Let the cakes cool in the pans for 10 minutes, then transfer to wire racks to cool completely.
07 - Whisk the instant vanilla pudding mix and cold milk together in a bowl for 2 minutes. Allow to thicken for 5 minutes, then gently fold in the whipped cream. Refrigerate until ready to assemble.
08 - Place one cooled cake layer on a serving platter. Spread half of the pudding mixture evenly over the top. Arrange a layer of sliced bananas and sprinkle with crushed vanilla wafers.
09 - Place the second cake layer on top. Spread the remaining pudding mixture over the surface. Decorate with whipped cream, the remaining sliced bananas, and additional crushed vanilla wafers.
10 - Refrigerate the assembled cake for at least 2 hours to allow the flavors to meld and the layers to set before slicing and serving.