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 softened butter and granulated sugar together using 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 evenly distributed.
05 - Fold the mashed bananas into the batter. Then 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, smoothing 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 invert onto wire racks to cool completely before assembling.
08 - Whisk the instant vanilla pudding mix and cold milk together in a bowl for 2 minutes until smooth. Allow it to thicken for 5 minutes, then gently fold in the whipped cream. Refrigerate until ready to use.
09 - Place one cooled cake layer on a serving platter. Spread half of the pudding filling evenly over the top. Arrange a layer of sliced bananas and sprinkle with a portion of the crushed vanilla wafers.
10 - Position the second cake layer on top. Spread the remaining pudding filling over the surface. Finish with whipped cream, the remaining banana slices, and crushed vanilla wafers for garnish.
11 - Refrigerate the assembled cake for at least 2 hours to allow the flavors to meld and the layers to set before slicing and serving.