Step 1: Prepare the Baking Pan
Preheat your oven to 350°F (175°C). Grease and flour a 9-inch round or square baking pan, or line it with parchment paper for easy removal.

Step 2: Mix Dry Ingredients
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.

Step 3: Cream Butter and Sugars
In a large mixing bowl, use an electric mixer to cream the softened butter with the granulated sugar and brown sugar until light and fluffy (about 2-3 minutes).

Step 4: Add Eggs and Vanilla
Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract to combine.

Step 5: Add Bananas and Buttermilk
Fold in the mashed bananas until incorporated. Add the dry ingredients and buttermilk alternately, beginning and ending with the flour mixture. Mix gently to avoid overmixing, as this can make the cake dense.

Step 6: Bake the Cake
Pour the batter into the prepared pan and spread it evenly. Bake in the preheated oven for 35-40 minutes, or until a toothpick inserted in the center comes out clean. Let the cake cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.

Step 7: Prepare the Pudding Topping
While the cake cools, prepare the pudding topping. In a medium bowl, whisk together the milk and instant pudding mix until thickened, about 2 minutes. For extra creaminess, fold in whipped cream or whipped topping.

Step 8: Assemble the Cake
Once the cake is cool, spread the pudding mixture over the top. Let the cake sit in the refrigerator for at least 30 minutes to allow the flavors to meld and the pudding to set.

Step 9: Garnish and Serve
Before serving, sprinkle crumbled vanilla wafers or nuts over the pudding layer, and add fresh banana slices if desired. Slice and enjoy!