Preheat the oven to 350°F (175°C). Grease and flour a 9×13-inch baking pan.
In a large mixing bowl, cream the butter and sugar until light and fluffy. Beat in the eggs one at a time, then stir in the vanilla.
In a separate bowl, combine the flour, baking soda, and salt. Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the mashed bananas and sour cream. Pour the batter into the prepared pan and spread it out evenly.
Bake for 25-30 minutes or until a toothpick inserted into the center comes out clean. Let the cake cool completely.
For the pudding layer, in a saucepan, whisk together the sugar, cornstarch, and salt. Gradually whisk in the milk and egg yolks.
Cook over medium heat, stirring constantly until the mixture thickens and boils. Remove from the heat and stir in the butter and vanilla extract.
Let the pudding cool slightly, then pour it over the cooled cake, spreading it out evenly. Refrigerate for at least 1 hour.
For the topping, whip the heavy cream with the powdered sugar and vanilla extract until stiff peaks form. Spread the whipped cream over the pudding layer.
Garnish with banana slices and vanilla wafers before serving. Enjoy!