Preheat oven to 350 F. Bring a pot of water to a boil.
In a double boiler pot or tempered bowl, mix the flour and sugar until well combined. Whisk in the milk and add the beaten egg yolks until well combined. Reserve the egg whites for the meringue. Place the double boiler or tempered bowl over the pot of boiling water, ensuring the water does not come in contact with the bottom of the pot or bowl. Cook until the mixture has thickened. It will take about 20 - 25 minutes. You will need to stir the mixture more constantly as it begins to thicken. Once thickened, remove from heat and add the vanilla extract.
In a stand mixer, beat the 3 reserved egg whites until they have formed stiff peaks. You can tell the peaks are still when they cling to the sides of the bowl and stay in the bowl when turned upside down. Gradually, add the sugar and cream of tarter.
Slice the bananas into 1/4 inch slices. In an 8x8 or 11x7 pan, layer the vanilla wafers with the banana slices. Pour the pudding mixture over the wafers and bananas. With a knife swirl the pudding mixture around to ensure the wafers and banana slices are well coated. Spoon the meringue over the pudding, wafers, and bananas, covering the entire surface and sealing the edges of the baking dish. Bake in the oven for 15 minutes or until the meringue is golden brown.