Make the vanilla pudding: In a medium saucepan, combine the milk and vanilla paste and whisk over medium heat, being careful not to let the milk boil.

Meanwhile, in a bowl, whisk together the sugar, flour, salt, egg yolks and whole egg, then whisk the cream. Pour a few tablespoons at a time of the hot milk into the egg mixture, whisking between additions, until the mixture becomes loose enough to pour. Return the mixture to the saucepan and place over medium-low heat. Cook, stirring constantly so that you don’t scorch the bottom, until the mixture thickens into pudding, 10 to 15 minutes. It should coat the back of a wooden spoon.

Once thickened, remove the pan from the heat and strain the pudding through a sieve into a bowl to remove lumps. Cover the surface of the pudding with plastic wrap and let cool to room temperature.

Make the Chantilly cream: In a stand mixer fitted with the whisk attachment (or in a large bowl with an electric mixer), beat the cream, powdered sugar and vanilla on medium speed until you have stiff peaks (meaning when you remove the whisk from the cream, the whipped cream makes a point that stands straight up). Refrigerate the whipped cream until ready to use (up to 4 hours).

Assemble the banana pudding: Arrange a layer of whole Nilla wafers over the bottom of an 8-inch square baking pan or dish. Spread the cooled vanilla pudding on top of the cookies, making the layer as even as you can. Add the sliced bananas over the pudding, then spread the whipped cream over the bananas. Garnish the top with more crumbled vanilla wafers.

Cover the pudding with plastic wrap and refrigerate for at least 1 hour before serving or up to 4 days.