In a medium saucepan, combine the egg yolks, sugar, and flour. Whisk these ingredients together until well blended. Gradually pour in the whole milk while continuing to whisk, ensuring there are no lumps.
Place the saucepan over medium heat and cook the mixture, stirring constantly until the custard thickens enough to coat the back of a spoon. Remove from heat.
Stir in a pinch of sea salt and the vanilla extract. Mix well to combine flavors.
In a separate bowl, beat the egg whites until stiff peaks form, creating a light and airy texture.
Gently fold the whipped egg whites into the custard mixture, being careful not to deflate the egg whites.
In a 9x13 inch baking dish, layer vanilla wafers, sliced bananas, and custard. Repeat layers, finishing with a custard layer on top.
Cover with plastic wrap and refrigerate for at least 4 hours or overnight to allow the pudding to set.
Before serving, whip your favorite whipped cream and spread it generously over the top of the pudding.