To prepare the cake:

1. Preheat the oven to 350 degrees  and prepare a 9×13” metal baking pan with baking spray.
2. In the clean bowl of a stand mixer, using the whisk attachment, whip the four egg whites on medium-high speed until stiff peaks form. Scoop out of the bowl and set aside while you prepare the rest of the cake.
3. Using the paddle attachment in the bowl of the same stand mixer, cream the butter on medium speed until smooth, about 1 minute. Add the oil and sugar and cream until light and smooth, about 2 minutes. Add the vanilla extract and stir to combine. In a separate smaller bowl, stir together the flour, baking powder, and salt. Add half of these dry ingredients into the butter mixture and stir on low to combine. Add the milk, stirring to combine, followed by the remaining dry ingredients. Stir on low until well incorporated.
4. Use a rubber spatula to gently fold in the egg whites until well incorporated, being careful to not overmix. Spread the cake batter into the prepared pan and bake until toothpick insereted comes out clean, about 20-25 minutes. Take care to not overbake as the cake will be dry if so.
5. When done, remove from oven to cool all the way while you prep your pastry cream.

To prepare the pastry cream:

1. In a medium saucepan, combine 1-1/4 cups of milk, the sugar, and salt. Cook over medium heat, stirring regularly to bring to a simmer and dissolve the sugar. In the meantime, in a separate bowl, stir together the remaining ¼ cup milk with the cornstarch, flour, and egg yolks. Whisk to combine and set aside while waiting for the milk and sugar mixture to simmer. Once the milk and sugar mixture is barely bubbling, remove from heat and slowly pour it in a small and steady stream into the cornstarch mixture, whisking vigorously. Continue streaming in while whisking until all the hot milk has been incorporated and then return the whole lot of it back into the saucepan. Whisk constantly over medium heat until barely bubbling and the mixture has thickened to a mayonnaise consistency. Remove from heat and stir in the butter and vanilla until smooth. Immediately move to assemble the cake.

To assemble the cake:

1. Space out a single layer of thin banana slices on the cooled cake. Pour the hot pastry cream on top of the bananas and use a spatula to spread it all over the top evenly. Try to keep it on top of the cake instead of falling off the sides. Place a single sheet of plastic wrap directly on top of the pastry cream and place in the fridge to cool, about 30 minutes.
2. Once cool, pour the heavy whipping cream into a large bowl or the bowl of a stand mixer. Whip on medium speed until slightly thickened and frothy. Add the sugar and continue whipping until stiff peaks form. Carefully remove the plastic wrap from the top of the pastry cream and  spread the whipped cream over the top of the entire cake. Serve immediately with additional slices of banana or a crumble of graham crackers.