01 - Preheat oven to 350°F. Grease and flour two 9-inch round cake pans.
02 - In a bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
03 - In a large mixing bowl, beat the butter and sugar together until light and fluffy. Add the eggs one at a time, beating well after each addition, then stir in the vanilla extract.
04 - Mix in the mashed bananas. Alternate adding the flour mixture and buttermilk to the batter, beginning and ending with the flour mixture. Stir until just combined.
05 - Divide the batter evenly between the prepared pans and smooth the tops. Bake for 28 to 32 minutes, or until a toothpick inserted in the center comes out clean. Cool in the pans for 10 minutes, then transfer to wire racks to cool completely.
06 - Whisk the instant pudding mix and cold milk together in a bowl for 2 minutes. Let thicken for 5 minutes, then gently fold in the whipped cream. Chill until ready to assemble.
07 - Place one cooled cake layer on a serving platter. Spread half the pudding mixture over the top. Layer with sliced bananas and a sprinkle of crushed vanilla wafers.
08 - Place the second cake layer on top and spread the remaining pudding mixture over it. Decorate with whipped cream, the remaining banana slices, and additional crushed wafers.
09 - Refrigerate the assembled cake for at least 2 hours before serving to allow the flavors to meld and the layers to set.