Preheat the oven to 350 degrees F.
In a medium bowl, whisk the sugar, flour and salt together.
Whisk in a ½ cup of the milk and the egg yolks.
Place the remaining 3 cups of milk in a sauce pan and bring to a simmer, stirring frequently.
Whisk 1 cup of the hot milk into the egg mixture.
Add the egg mix into the rest of the milk on the stove and whisk together.
Bring to a low boil, stirring continuously, and cook until thick.
Add the butter and vanilla, stirring until the butter is completely melted. Set aside to cool while preparing the rest of the ingredients.
This can be made in a 9x13, but traditionally it is made in a tall, round glass bowl. In the 9x13 there will be in one layer, in a taller bowl you will probably make 3 layers.
Assemble this in layers with vanilla wafers on the bottom, followed by banana slices, and then put pudding over the banana, spreading it evenly with a spatula.
To make the meringue, put the egg whites and cream of tartar in a large bowl and beat with a hand mixer on high until you get soft peaks.
Add the sugar, a little at a time and continue mixing on high until you get stiff peaks.
Spoon the meringue over the pudding, completely covering to the edges.
Bake in the oven until the meringue is lightly browned. This will take ~15 minutes.
Garnish with the remaining vanilla wafers placed in the meringue, and let cool for 10 minutes before serving.