Prep your pans and oven. Heat oven to 350°F (175°C). Grease and line two 8- or 9-inch round cake pans with parchment.
You can also use a 9x13-inch pan if you prefer a sheet cake.
Whisk the dry ingredients. In a large bowl, whisk flour, baking powder, baking soda, and salt. Set aside.
Mash the bananas. In a separate bowl, mash the ripe bananas until mostly smooth. Whisk in buttermilk and vanilla.
Cream the fats and sugar. With a mixer, beat butter, oil, granulated sugar, and brown sugar until light and fluffy, about 2–3 minutes.
Add eggs one at a time, mixing well after each.
Combine wet and dry. Mix in half the dry ingredients, then the banana mixture, then the remaining dry ingredients. Stir just until combined. Do not overmix.
Bake. Divide batter evenly between pans.
Bake 22–28 minutes for round layers, or 30–35 minutes for a 9x13. The cake is done when a toothpick comes out clean with a few moist crumbs.
Cool completely. Let cakes cool in the pans for 10 minutes, then turn out onto a rack to cool fully. Cold layers are easier to frost.
Make the pudding. Whisk instant pudding mix with cold milk for about 2 minutes until thick.
Chill to set. It should be spoonable, not runny.
Make the whipped cream frosting. Beat the cream cheese until smooth. Add cold heavy cream and powdered sugar and whip to medium-stiff peaks.
It should be fluffy but hold its shape. Fold in 1 teaspoon vanilla if you like.
Layer the cake. Place the first cake layer on a plate. Spread a thin layer of whipped cream, then spoon a layer of pudding over it, staying 1/2 inch from the edge.
Sprinkle a generous handful of crushed vanilla wafers over the pudding.
Add the second layer. Top with the second cake round. Frost the top and sides with the remaining whipped cream frosting. For a sheet cake, spread pudding over the cake and top with whipped cream, then wafers.
Decorate. Press more crushed wafers onto the sides or sprinkle on top.
If using fresh banana slices, brush them with lemon juice and add just before serving.
Chill before serving. Refrigerate at least 1 hour. Chilling helps the layers set and makes neater slices.