01 - Preheat oven to 350°F. Grease and flour two 9-inch round cake pans, tapping out any excess flour.
02 - In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Set aside.
03 - In a large mixing bowl, beat the room-temperature butter and granulated sugar with an electric mixer on medium speed until pale, light, and fluffy, about 3 to 4 minutes.
04 - Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract until fully incorporated.
05 - Blend the mashed bananas into the batter. Alternate adding the flour mixture and the buttermilk in three additions, beginning and ending with the flour. Stir gently until just combined — do not overmix.
06 - Divide the batter evenly between the two prepared cake pans and smooth the tops with a spatula. Bake for 28 to 32 minutes, or until a toothpick inserted into the center of each layer comes out clean.
07 - Let the cake layers cool in their pans for 10 minutes, then turn them out onto wire racks to cool completely.
08 - Whisk the instant vanilla pudding mix and cold milk together in a bowl for 2 minutes. Allow the mixture to thicken for 5 minutes, then gently fold in the whipped cream. Refrigerate until ready to assemble.
09 - Place the first cake layer on a serving platter. Spread half of the pudding filling evenly over the top. Arrange a layer of sliced bananas and a sprinkle of crushed vanilla wafers over the pudding.
10 - Set the second cake layer on top. Spread the remaining pudding filling over the surface. Pipe or spoon the additional whipped cream on top, then garnish with the remaining banana slices and crushed vanilla wafers.
11 - Refrigerate the assembled cake for at least 2 hours to allow the flavors to meld and the pudding to set before slicing and serving.