Combine flour, sugar and salt in a large, heavy saucepan.
Lightly beat egg yolks and combine with milk in a large bowl or measuring cup. Pour the egg and milk mixture into dry ingredients in heavy saucepan. Cook over low to medium heat, stirring constantly, until ingredients are thickened and smooth. Remove saucepan from heat and stir in vanilla.
To layer your banana pudding, begin by placing vanilla wafers on the bottom of a 2 quart oven-safe glass bowl or baking dish.
Slice bananas and place on top of wafers.
Pour one-third of custard over wafers and bananas.
Repeat layering process two more times until all wafers, bananas, and custard have been used, ending with a final layer of wafers.
For the Meringue:
Whip egg whites with an electric mixer set at high speed.
Allow egg whites to foam, add cream of tartar and then gradually add sugar one tablespoon at a time.
Continue whipping until sugar is well-dissolved.
Add vanilla once stiff peaks have formed and whip until well-combined.
Spread meringue over banana pudding, making sure to spread to the edges of the dish.
Bake for about 25 minutes until the meringue is lightly browned.