Preheat oven to 350 degrees F.
Line the bottom of a 9 x 9 inch 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 custard.
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 (use fork or wisk 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. (If you're working with an electric cook top, 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 skimp, put one slice of banana per wafer, or closely edge to edge of the dish. Pour, spreading as necessary, half of the custard 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 tarter. At high speed, gradually add the sugar, a tablespoon at a time, and beat until siff peaks from. Fold the vanilla into the meringue, and spread the meringue over the pudding, sealing it to the sides of the dish.
Bake in a preheated 375 degrees F oven until meringue browns, 12 to 15 minutes, depending upon your oven.