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Fill a large saucepan one-third of the way with water and bring to a boil. Whisk the egg yolks in a small bowl and set aside.
Combine the flour, sugar and salt in a metal bowl large enough to fit neatly over the saucepan. Place it over the saucepan of boiling water and reduce the heat to medium low. Briskly stir in the half-and-half and cook until the mixture begins to thicken slightly. Add the egg yolks and continue stirring, scraping the sides as you go. As the pudding begins to thicken slightly again (and all the lumps are gone), add the heavy cream and continue to cook, stirring constantly, over medium to medium-low heat until the mixture resembles a quite thick pancake batter, 20 to 30 minutes. Note: It is imperative that you constantly monitor the heat to ensure the pudding thickens properly without scalding. If it gets too hot, it will curdle, from which there is no recovery. So be patient. It will be worth it. Let the pudding rest off heat for 30 minutes or so, then stir in both kinds of vanilla.
To assemble: Layer the ingredients, starting and ending with the vanilla wafers, in a serving bowl. Start by lining the bottom of your serving bowl with the wafers. Slice the bananas and evenly distribute over the wafers for the next layer, Whisk the pudding briefly, then immediately ladle it over the bananas (to minimize oxidation), thickly enough to completely cover the bananas but not so much that they're swimming in it. Continue layering to the top of the serving bowl, ending with the wafers on top.
Cover the serving bowl with plastic wrap, gently pressing the wrap down so it actually touches the top of the pudding and seals it (this prevents rubbery crust from forming on top as it chills). Chill thoroughly in the refrigerator before serving, at least 2 to 3 hours.