Preheat the oven to 350 degrees F.
Coat a 19x13-inch baking pan with cooking spray.
In a medium bowl, sift together 2 1/2 cups of the flour, the baking powder, the cinnamon, 3/4 teaspoon of the salt, and the baking soda.
In a large bowl, use an electric mixer to beat 2 cups of the granulated sugar, 3 of the eggs, the oil, the buttermilk, and 1 teaspoon of the vanilla together on medium speed until combined, about 2 minutes.
Add the flour mixture to the sugar mixture, 1/3 at a time, and beat after each addition, on low speed just until smooth.
Fold 1 1/2 cups of the mashed bananas into the batter.
Transfer the batter into the prepared baking pan and bake until a toothpick inserted in the center comes out clean, about 30-35 minutes.
Transfer the pan to a wire rack and allow the cake to cool for 10 minutes.
Using the handle of a wooden spoon, poke deep holes all over the cake, about 5 across and 6 down, totaling 30 holes.
While the cake is cooling, in a large saucepan, whisk 1/2 cup of the sugar, the cornstarch, and the salt to taste together.
Whisk the milk into the sugar-cornstarch mixture.
Whisk 2 of the egg yolks into the sugar-cornstarch mixture until well blended.
Bring the sugar mixture to a boil over medium heat, stirring constantly.
Immediately reduce the heat to low and simmer, stirring constantly, until the pudding is thick enough to coat the back of a spoon, about 1-2 minutes.
Pour the pudding through a fine wire-mesh strainer into a large bowl.
Whisk the vanilla bean paste and 1/2 tablespoon of the butter into the pudding.
Allow the pudding to cool, stirring occasionally, until lukewarm, about 15 minutes.
Spread the pudding evenly over the cake.
Cover the cake with plastic wrap, pressing it directly onto the pudding (to prevent a skin from forming) and chill in the fridge for at least 2 hours and up to overnight.
Preheat the oven to 350 degrees F.
Discard the plastic wrap from the cake.
Scatter the slices from the remaining bananas evenly over the pudding.
In a large bowl, using an electric mixer, beat the heavy cream, the powdered sugar, and the remaining vanilla on medium-high speed until thick and spreadable.
Spread the whipped cream over the banana slices, covering the cake in an even layer.
In a small bowl, stir the vanilla wafers, the remaining melted butter, the remaining flour, and the remaining granulated sugar together.
Press the wafer mixture with your figures to form small clumps.
Spread the wafer clumps onto a baking sheet.
Bake the wafer clumps until crisp and brown, about 5-6 minutes.
Allow the wafer topping to cool completely, about 5-6 minutes.
Sprinkle the wafer topping over the whipped cream topping.
Slice and serve immediately.