Preheat oven to 350°F (175°C). Grease and flour two 9-inch round cake pans or a 9×13-inch pan.

1. In a large bowl, whisk together flour, sugar, baking powder, baking soda, and salt.
2. In another bowl, combine eggs, mashed bananas, oil (or butter), buttermilk (or sour cream), and vanilla extract.
3. Stir wet ingredients into the dry ingredients until just combined.
4. Pour batter into prepared pans and bake for 25–30 minutes, or until a toothpick inserted comes out clean.
5. Let cakes cool in the pans for 10 minutes, then transfer to a wire rack to cool completely.
6. Prepare pudding: whisk vanilla pudding mix with cold milk until thickened.
7. Place one cake layer on a serving plate. Spread with half the pudding and top with banana slices.
8. Add second cake layer and frost the top and sides with whipped topping.
9. Chill the cake for 1–2 hours before serving. Garnish with crushed vanilla wafers or banana slices, if desired.