Follow the instructions to make my all-time Favorite Pastry Cream, following the instructions (step #9 in the recipe) to chill the cream for at least 3 hours, and up to 48 hours.
Heat the oven to 350 degrees F (176 degrees C). Grease the inside of a 10-inch (12-cup) bundt pan with vegetable shortening or butter. Sprinkle flour inside the pan and shake it around so that the entire inside of the pan is coated with flour.
Add the cake flour, baking powder, baking soda, salt, nutmeg, and ginger to a large bowl and stir with a wire whisk to combine.
Beat the butter, vegetable oil, and brown sugar with an electric mixer on medium-high speed until the mixture is light and fluffy, about 4 minutes. Add the eggs and egg yolk one at a time, beating on medium-high speed after each addition until fully incorporated.
Beat in the vanilla, then the mashed banana, beating until well combined.
Mix in the buttermilk and flour mixture in alternating additions, starting and ending with the flour: Flour, buttermilk, flour, buttermilk, flour. Beat in each addition on low speed, mixing just long enough to barely incorporate one addition before adding the next. Be careful to not over-mix.
Pour the batter into the prepared pan, smoothing out the top with a rubber spatula or wooden spoon.
Bake the cake in the center of the oven for 50 - 60 minutes. The cake is done when it's pulled away from the sides of the pan and a toothpick inserted in the center of the cake comes out without any raw batter on it.
Remove the cake from the oven and let it cool inside the pan for 5 minutes. Gently turn it out of the pan onto a wire rack and let it cool completely before filling and frosting.
Beat the cream cheese, butter, vanilla, salt, and 4 cups powdered sugar with an electric mixer on low just until blended. Turn the mixer up to medium-high and beat for 2-3 minutes, until creamy and smooth. Add more powdered sugar if necessary to achieve a spreadable consistency.
After beating the whipped cream into the pastry cream (steps 10 and 11 in the pastry cream recipe), beat in the mashed banana.
Fit a pastry bag with a large round or star-shaped decorator tip (see links below) and fill it with pastry cream. Set the cake upside down on a work surface.
Poke the decorator tip into the cake and squeeze some filling into it. The surface of the cake's bottom will split slightly as you do this and that's ok. Just be careful to not insert so much pastry cream that the sides and top of the cake begin to split. *See photos above.
Continue to move around the cake, filling the entire center of the cake with pastry cream. Again, see the photos above for reference.
Carefully turn the cake over onto a plate or cake stand. Cover the cake with cream cheese buttercream and then sprinkle crushed vanilla wafers over the buttercream.
Serve each slice of cake with an additional dollop of banana pastry cream.
