01 - Preheat oven to 350°F. Grease and flour two 9-inch round cake pans, then line the bottoms with parchment paper.
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 until light and fluffy, about 3 minutes.
04 - Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract until evenly combined.
05 - Fold in the mashed bananas. Alternate adding the flour mixture and buttermilk in three additions, beginning and ending with the flour. Stir until just combined — do not overmix.
06 - Divide the batter evenly between the two prepared pans and smooth the tops. Bake for 28 to 32 minutes, or until a toothpick inserted into the center comes out clean.
07 - Let the cakes cool in the pans for 10 minutes, then invert onto wire racks to cool completely.
08 - Whisk the instant vanilla pudding mix with cold milk in a bowl for 2 minutes. Allow it 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 the pudding filling over the top. Arrange a layer of sliced bananas and sprinkle with crushed vanilla wafers. Place the second cake layer on top and spread the remaining pudding filling over it.
10 - Top the cake with whipped cream, remaining banana slices, and additional crushed wafers. Chill for at least 2 hours before serving to let the flavors meld and the layers set.