- Preheat oven to 375°F.
- Line the bottom of a 9" x 9" baking dish with a layer of vanilla wafers.
- Peel the bananas and slice into 3/8-inch rounds. Cover the banana slices with plastic wrap to keep them from darkening and quickly make your pudding.
- Combine the sugar, flour and salt in a bowl, and stir well to mix. Mash out any flour lumps with the back of your spoon. Set aside.
- In a heavy saucepan, beat the egg yolks well (just use a fork or whisk, but beat them well). Over medium heat, add the flour mixture to the egg yolks, alternately with the milk and vanilla, stirring constantly. Bring to a gentle boil and, when the mixture begins to thicken, add the butter, continuing to stir. Keep boiling and stirring until mixture reaches a nice pudding consistency. [Note: If you're working with an electric cooktop, adjust the heat so that it's hot enough to boil, but not so hot that the pudding scorches.] Remove from heat.
- Place a layer of banana slices in the baking dish on top of the vanilla wafers. Don't stint and put one slice of banana per wafer. Line those banana slices up edge-to-edge. Pour, spreading as necessary, half of the pudding over the banana layer. Put down another layer of vanilla wafers, another layer of banana slices, and cover with the remaining pudding.
- Beat the egg whites at high speed until they form soft peaks. Add the cream of tartar. At high speed, gradually add the sugar, a tablespoon at a time, and beat until stiff peaks form. Fold the vanilla into the meringue, and spread the meringue over the pudding, sealing it at the sides of the dish.
- Bake in a preheated 375°F oven until meringue browns, 12 to 15 minutes, depending upon your oven.